Papers

We develop a data-driven approach to dynamic portfolio selection that combines vine-copula simulation with reinforcement learning. The investor has constant relative risk aversion and maximises expected terminal utility with a running penalty on the conditional value-at-risk (CVaR) of one-period losses. We estimate a conditional vine model from historical returns and use it to generate joint scenarios for CVaR evaluation and conditional paths for training a recurrent portfolio policy. Under uniform local derivative bounds, we propagate edgewise pair-copula parameter errors through the conditional transforms to obtain power-law stability bounds in Hellinger distance and total variation. In a finite-horizon investment model, we combine these estimates with a marginal and structural approximation budget to bound policy values, optimal values and the true-market loss of policies selected under a fitted model, with separate simulation and numerical optimisation terms. On a seven-asset panel comprising US and Chinese equities and gold, the selected ensemble of ten trained policies achieves a compound annual growth rate of 34.13% and a Sharpe ratio of 2.31 over 22 complete monthly holding periods, exceeding the corresponding values of six classical and vine-based benchmarks. Combining simulated and historical training data reduces monthly target-to-target turnover by 41.5% relative to training on historical data alone, while maintaining comparable growth.

Tolls for safe passage and attacks on shipping are usually treated as mutually exclusive: either ships pay or attacks happen. We argue they are complementary. In a Stackelberg escalation game for the Strait of Hormuz, the enforcer chooses an attack intensity and a toll schedule; the response is to pay, cross exposed, wait, reroute, or exit. Attacks create the willingness to pay; tolls harvest it. The model predicts asymmetry across trade forms: a toll where the cargo owner can pay and the vessel owner will consent, and none where either fails. Any such payment is clandestine, but the model's implications are testable against freight rates, insurance premia, and incident reports.

The most widely used investment risk measures - variance, standard deviation, and tracking error - treat upside deviations as equally undesirable as downside losses. In stable markets with assumed symmetric return distributions, this simplification is potentially harmless. In the climate transition age, it is not. Climate risk is two-dimensionally asymmetric, across assets and over time. Both dimensions are negatively skewed against investors. Hence, climate transition investment strategies deliberately deviate from benchmarks that reflect an insufficiently decarbonising global economy. When fiduciaries enforce tracking error budgets that penalise outperformance just as heavily as underperformance, they inadvertently constrain exactly the portfolio return opportunities that climate-aware investing seeks. We argue that replacing symmetric deviation-based risk measures with their downside-only counterparts - semi-variance, standard risk and trailing error - resolves this conflict without sacrificing any fiduciary discipline. The distinction is not merely semantic: as the gap between climate transition trajectories and market benchmarks widens over the coming decades, symmetric risk budgets will become binding constraints on transition strategies well before actual investment risk warrants it. We propose specific changes to mandate design that would allow institutional investors to pursue climate transition opportunities within genuinely risk-aware (rather than deviation-averse) frameworks.

We study dynamic portfolio decarbonization under incomplete information about firms' carbon intensities and the underlying transition state. The investor maximizes expected utility of terminal wealth net of a penalty on perceived cumulative financed emissions. Asset returns and carbon intensities depend on a stochastic transition factor, while the investor may need to infer the current transition state, its long-run mean and firms' carbon intensities from market observations and periodic noisy disclosures. The optimal strategy combines a Merton-type component with climate-dependent expected-return adjustments, a direct carbon intensity penalty and intertemporal hedging demands associated with stochastic carbon intensities and learning. In a numerical application, incomplete information has limited effects on welfare and target satisfaction when prior beliefs are well specified. By contrast, biased beliefs generate welfare losses in either direction but asymmetric environmental consequences: optimistic and pessimistic beliefs induce opposite portfolio tilts and therefore affect the probability of exceeding the cumulative emissions target differently.

In stochastic control problems involving optimal portfolio choice, one often seeks an optimizer of some local criterion (dynamic programming value function) generated by some global criterion (e.g., expected utility). The local optimizer then typically acts as a stochastic integrand with respect to some multivariate stochastic process (e.g., asset prices). This paper takes a closer look at local criteria in the form of “local expected utility”. Since the existence of the local optimizer can be established under very mild conditions, it is crucial to understand under what circumstances the local optimizer has good integrability properties. It is shown that the reasonable asymptotic elasticity condition of Kramkov and Schachermayer (1999) applied to the local utility function plays a key role in this context.

Households compare their living standard with others' and dislike changing it. We study consumption and investment when felicity depends on consumption relative to a benchmark, the population's geometric average consumption, and cuts in felicity weigh more than increases. Asset returns are exogenous. For finitely many types and arbitrary initial wealth and inherited standards, a mean field equilibrium exists under a weak interaction condition, and for fixed budget multipliers the benchmark is the fixed point of a contraction. In a complete market with common risk, a mean field equilibrium at empirical type frequencies is an exact Nash equilibrium of the finite game, for any preferences over relative consumption. We bound the gain from deviating when plans computed at another composition are used. We compute equilibria in which groups with different wealth, inherited standards, and loss aversion revise spending at different dates. With identical households and common risk, the unique symmetric equilibrium is the policy of a single loss averse household with modified curvature. In a baseline example, ignoring the inherited standard costs up to 17% of wealth, while small errors about the composition of the reference group cost less than 0.5%.

To extend conventional model-level feature importance to economically meaningful portfolio outcomes and decisions, we propose a local first-order attribution-propagation framework that maps allocation-function feature exposures to local sensitivities of sequential portfolio performance metrics. We relate the propagated attributions to Shapley values defined directly for portfolio objectives and derive statistical inference for Sharpe-ratio attributions. The resulting attribution-guided feature-exposure intervention enables post-training adaptation, translating portfolio-metric explanations into out-of-sample decisions without retraining the underlying allocation model. We further introduce temporal stabilisation and cross-model averaging as complementary regularisation mechanisms. Empirically, the interventions yield statistically significant improvements in net Sharpe ratios across different model classes.

Formulaic alpha mining seeks to discover executable expressions that capture predictive market signals in a vast, noisy search space. Recent LLM-based approaches use prompting, iterative search, or seed-factor evolution, leaving direct factor construction through policy learning less explored. To address this, we introduce AlphaRLM, a reinforcement-learning framework that trains LLMs to construct executable symbolic factors from financial literature without input factor expressions. AlphaRLM incorporates Literature-Guided Operator Assembly (LEGO), which conditions factor construction on literature-derived ideas and executable operators, providing semantic priors for exploration. It further aligns the generation policy with market feedback through executable-validity and grouped-return-separation rewards that capture non-monotonic structures across factor quantiles. Extensive experiments on CSI 300, CSI 1000, and S&P 500 show that AlphaRLM outperforms strong factor-mining and LLM-based baselines in annualized excess return. Notably, the 8B model achieves strong cross-market performance, highlighting the promise of literature-conditioned, market-aligned factor generation.

Portfolio decisions are often made under uncertainty about expected returns, and investors revise their beliefs as new information arrives. Although richer information generally cannot reduce optimized value ex ante, the trading strategy it induces need not improve on the strategy induced by a less informative information structure in every fixed-drift scenario. We introduce scenario-conditional expected utility and value of information to evaluate strategies selected under the investor's current belief. In a finite-horizon Gaussian portfolio choice model, we compare a fixed-belief investor, a price observer, and an attentive investor who also processes an auxiliary signal under an attention capacity constraint. Ex ante, price learning and auxiliary attention are valuable, and the total value of attention increases with capacity. Scenario-conditionally, learning creates a correction benefit by reducing the initial trading-position gap relative to the full-information strategy, but also a fluctuation cost through belief revisions, so the ex ante ranking can reverse. We derive the current-belief distribution of scenario-conditional value and the associated underperformance probability, defined as the probability of negative scenario-conditional value relative to fixed-belief choice. Over sufficiently short horizons, the scenario-conditional value of learning is negative when belief error is small relative to posterior uncertainty. For a given horizon, sufficiently high attention capacity yields a higher scenario-conditional value than any fixed finite-capacity benchmark across all drift scenarios. We also derive sharp convergence rates to full-information performance under Shannon and Tsallis technologies.

This paper studies entropy regularization for the discrete-time dynamic mean–variance portfolio problem with no-shorting constraints. In the unconstrained setting, entropy regularization can be introduced without changing the basic quadratic structure of the dynamic program. Under no-shorting, this property is lost: a standard fixed-temperature formulation generally preserves convexity but no longer preserves the homogeneous Bellman structure and the associated piecewise-linear feedback form. We introduce a state-dependent temperature that is matched to the homogeneity of the original mean–variance problem. This restores the piecewise-quadratic value function and the finite-dimensional Bellman recursion. The resulting formulation, however, makes convexity depend on the continuation coefficients generated by the soft recursion. We show that negative continuation coefficients lead to loss of convexity and prove that a common sufficiently small temperature preserves the Bellman structure and convexity over the entire finite horizon. The original no-shorting solution is recovered as the temperature vanishes. We also develop a sample-based implementation for unknown return distributions. Numerical and empirical results illustrate both the structural advantage of the state-dependent temperature and the practical relevance of the convexity-preserving temperature restriction.

We represent (weighted-)selection-elliptical distributions as an affine combination of the $q$ selection variables plus an elliptical term whose direction alone is independent. This form suffices for $q+2$ fund separation via first-order stochastic dominance, inter alia relaxing Simaan's (1993) three-fund assumptions.

As option markets grow and AI advances, agentic systems for option trading are gaining increasing attention. Language-model-based agents can reason over contextual information such as news, but option trading presents a particularly challenging decision problem: a single stock can have thousands of contracts, and the agent must decide both which contracts to trade and how to combine them. Existing approaches often sidestep this complexity by restricting the policy to a fixed strategy structure, such as a straddle, limiting their ability to switch strategies as market conditions change. We present SOTA (Stock Options Trading Agents), an agentic trading framework for structured option-strategy selection. SOTA abstracts the large option universe into strategy-level decisions while deterministic resolvers handle portfolio implementation. We develop SOTA by post-training Qwen3.8-27B with supervised fine-tuning followed by reinforcement learning. SOTA is evaluated on options on nine large-cap U.S. equities and SPY against rule-based and machine-learning strategy selectors in the same trading environment. Over a six-month out-of-sample period, SOTA earns an 18.3% total return with a Sharpe ratio of 1.60 and a maximum drawdown of 8.96%. We also document an asymmetric role of news: news improves frontier-teacher trajectories, but retaining news during reinforcement learning reduces out-of-sample return from 18.3% to -2.7%.

Reality may establish that an outcome occurred without identifying which evolving procedure produced it or why. This distinction matters in production ML systems whose code, configuration, and artifacts change while external feedback accumulates. We examine it in a human-directed, agent-engineered quantitative trading system, using oracle to mean an external source of realized outcomes rather than a complete correctness specification. Across one year, the account gained and outperformed a broad market index, while annual alpha was not statistically distinguishable from zero under the main retrospective specification. Retrospectively selected subperiods include adverse relative performance and conditional candidate-level weakness under declared approximate references. Engineering records document changes during the episode, and complete recommendation-to-runtime binding is unavailable. The archive does not establish a common frozen instance or a unique cause. The case motivates an outcome–diagnosis gap: outcome evidence, evaluated-object identity, and causal explanation support distinct claims. We distinguish frozen instances, pre-specified adaptive procedures, and ad-hoc development; organize archive-relative claim identifiability and an evidence hierarchy; and propose a prospective production-binding protocol. An illustrative compatible-history example shows how factual binding can resolve a recommendation's referent without supplying its counterfactual effect. The protocol is proposed rather than prospectively validated. External feedback constrains outcome claims, while provenance and additional identification structure determine the resolution of diagnosis.

In this paper, we present robust portfolio selection models by incorporating a reward and penalty mechanism into portfolio management. We assume that the joint distribution of the losses of the underlying risky assets in a portfolio is uncertain but lies within a multivariate distribution set. Our goal is to identify optimal portfolio allocations by minimizing the worst-case conditional value-at-risk (CVaR) of portfolio loss under the reward and penalty mechanism and distribution uncertainty. Our models can also be used to investigate the problem of how to balance portfolio losses with their associated downside risk in portfolio management. We first derive an explicit closed-form expression for the worst-case CVaR under the reward-penalty mechanism, which generalizes several existing models and results regarding the worst-case CVaR, such as those studied in Jagannathan (1977), Chen et al. (2011), and Cai et al. (2024). We then apply this expression to obtain optimal portfolio allocations that minimize the worst-case CVaR under both a classical mean-covariance-based multivariate distribution set and a generalized mean-covariance-based multivariate distribution set introduced in Kang et al. (2019). Additionally, we utilize real market data to illustrate the application of the proposed models and the corresponding optimal portfolio allocations in portfolio management. Our empirical experiments show that portfolios based on the proposed models have the potential to outperform those based on several existing related models. Furthermore, the results demonstrate that incorporating downside risk into portfolio loss helps better manage risk and can achieve higher investment returns than considering either downside risk or portfolio loss alone. Moreover, our experiments reveal the trade-off between improving expected portfolio return and controlling the worst-case portfolio CVaR.

We investigate a continuous-time financial market where the asset price exhibits weak (sublinear) mean reversion and has a nonzero drift. Complementing earlier work on strong (superlinear) mean reversion, we show that, for an investor maximizing expected exponential utility, the certainty equivalent grows as $O(T^{2\beta+1})$ where $0<\beta<1$ is the strength of mean reversion. An explicit asymptotically optimal strategy is also given.

Factor mining seeks to discover signals from financial data that predict future asset returns and guide portfolio construction. Automated factor mining now spans genetic programming, reinforcement learning, generative models, and large language model agents. Yet it remains unclear whether advances across these paradigms yield more generalizable, distinct, and economically useful financial signals. We introduce FactorBench, a portfolio-aware benchmark comparing roughly five thousand mined factors from nine automated mining methods across five equity markets. A shared data and evaluation contract supports both symbolic expressions and executable Python factors, connecting heterogeneous discovery algorithms to common signal combination and portfolio construction procedures. FactorBench traces the outputs of mining systems across three levels: factor validity, temporal generalization, and predictiveness beyond measured risk and style exposures; within- and across-method pool distinctness, including similarity to the benchmark Alpha101; and composite-signal quality and after-cost long-only and long–short portfolio performance. After systematically assessing whether advances in factor mining translate into signal quality and portfolio performance, FactorBench finds that no paradigm consistently dominates.

The enhanced index tracking (EIT) portfolio selection problem aims to construct a portfolio that is expected to outperform a benchmark index. In practice, investors face uncertainty in the joint distribution of asset and index losses, as the true distribution is typically unknown and only partial information is available. Moreover, portfolio selection requires balancing the trade-off between mean loss and downside risk while targeting higher returns. Effectively modeling and managing these factors in EIT portfolio selection is therefore of both practical and research interest. To address these challenges, this paper proposes robust EIT portfolio selection models under distributional uncertainty, guided by Pareto-optimality theory. The models minimize a convex combination of worst-case mean loss and downside risk, subject to a constraint on worst-case mean return. Two uncertainty sets are considered: one assuming a known mean loss vector and covariance matrix, and a more general set with unknown moments. Closed-form solutions are derived for the former, while the latter reduces to tractable convex optimization problems. Empirical results based on real market data show that the proposed models outperform not only the tracked index but also the equally weighted portfolio, robust mean-variance models, and robust variance models in terms of out-of-sample cumulative wealth, as well as Sharpe, Sortino, and Omega ratios. Moreover, portfolios that minimize a convex combination of worst-case mean loss and downside risk consistently outperform those that minimize downside risk alone. We also provide practical guidance for selecting optimal weighting coefficients to effectively balance risk and return.

A cross-sectional signal is a forecast vector over $d$ assets at each date; demeaned and normalized, it is a point on a sphere. Its city is the direction of its time-averaged vector in a common target-aligned frame, a compressed summary. When is the angle between two cities a conservative estimate of the angle between the histories? For independent uniform histories, the probability that the history angle is at least the city angle tends to one when the city angle is at most 90 degrees, with an $O(T^{-1/2})$ error bound uniform in dimension. Selecting for positive average information coefficient (IC) changes the unconditional limit to $\gamma_q>1/2$, about 56% for 20 assets. The bound extends to independent, rotationally symmetric histories with temporal dependence; summable products of lag correlations preserve the conditional limit. A stationary ergodic theorem allows shared signal movement and identifies the population margin determining the limiting ordering. Among 266,815 positive-IC pairs in AlphaNova's Competition May 2026, the history angle is at least the city angle for 58.9% overall, 74.1% at city angles up to 90 degrees, and 1.5% beyond. These frequencies describe the observed library and do not validate the uniform null: residual agreement is mostly positive, and an empirical second-moment diagnostic cannot be matched within that null by adjusting temporal dependence alone. On the full 776-signal sample, a city angle of at least 60 degrees selects pairs with a 94.3% success rate at the same history-angle threshold, against an 85.0% base rate, and retains 72.5% of pairs. Explicit constructions show the limits of direction-only summaries, retained lengths give sharp bounds, and shared time blocks recover missing information, here only at fine resolution. Persistent positive IC confines cities and bounds their motion; convergence also requires a stable mean direction.

When developers change one component of an agent, such as its controller, a learned model or its verifier, they usually judge the change by an aggregate task score. That score cannot tell whether improvement was attainable, which component lost value, or what the agent's own checks certify. We introduce a claim-specific verification audit for modular agents that plan, act, check and refine. Instead of scoring the agent, the audit scores the evidence: each conclusion is recorded with the evidence behind it, one of four verdicts (supported, unsupported, unresolved or not evaluated) and the boundary within which it holds. Three tools supply that evidence. Oracle policies measure attainable improvement under an explicitly stated action set, so that a low value can be traced to the evaluation rather than to the environment. Replacing one component at a time with a perfect counterpart locates lost value, with null results read as unresolved whenever a downstream component could mask them. A separate test asks whether the verifier's score identifies the quantity it is read as bounding. Applied to a constrained portfolio-allocation agent in a synthetic market with known hidden regimes, the audit shows that the value of perfect regime information depends on the action set used to measure it, that the scenario generator discards most of the regime signal while better local fidelity does not improve decisions, and that the runtime verifier can be bypassed with no visible change in outcomes. The contribution is the protocol and the evidential distinctions it enforces; the empirical findings are specific to the agent and environment studied.

We develop a spouse-protected tontine in which a first death changes the household state but generates no pool transfer. The same account remains attached to the household contract until extinction and funds a spouse-only continuation phase if the retiree dies first. We derive contract-level actuarial-fairness conditions and a finite-pool mortality-credit allocation rule with exact ex post budget balance. Under a homogeneous large-pool approximation, we formulate a multidimensional decumulation problem for a representative household, with withdrawal and rebalancing controls while the retiree is alive. The objective balances expected cumulative real household payments against the Conditional Value-at-Risk (CVaR) of terminal shortfalls relative to household reserve targets, without conditioning on survival to the horizon. We develop a numerical solution method for this problem based on a global-in-time neural-network parameterization of admissible control policies. We quantify policy-induced spouse-continuation costs using expected-cost and risk-loaded payment-scale loads at both representative-contract and book levels. We characterize the large-book limit of average per-contract continuation cost as the expected representative-contract cost conditional on common market information. Numerical experiments calibrated to Australia show that the spouse-only phase is a first-order and persistent household event. In these experiments, book-level diversification removes most of the representative-contract excess upper-tail cost of spouse continuation in the large-book limit, without changing expected per-contract continuation cost. A cross-country mortality comparison indicates that the prevalence and persistence of the spouse-only phase are not specific to Australia.

Decision-focused learning (DFL) trains predictors through downstream objectives, but a different loss need not provide an independent parameter-update direction. We characterize this restriction through the predictor Jacobian, using sparse index tracking to distinguish the covariance entries read by the optimizer from the parameter directions available to learning. Rank-one Jacobians make nonzero per-example gradients collinear; a conditional spectral bound describes near-collinearity. A batch-subspace characterization and counterexamples show why these local statements imply neither common minimizers nor collinear batch updates. Experiments examine when geometry translates into decision quality. Across 38 one-parameter equity configurations, DFL gains over MSE remain below 1.8%; a 385-parameter conditional predictor also has pointwise rank one. In validation-tuned shortest-path and knapsack experiments, full-capacity SPO+ reduces mean regret by 11.6% and 10.6%, respectively; only knapsack survives correction across eight comparisons. The capacity contrast persists on fresh datasets across batch orders and training budgets. Holding expressivity fixed, invertible coordinate scaling lowers spectral effective rank and ordinary SGD gains; compensating for the scaling restores the original trajectories. Financial forward-target controls separate forecast accuracy from decision quality; a matched neural comparison finds no aggregate DFL advantage in the tested architecture. These findings distinguish local rank restrictions, coordinate-dependent optimization and predictive accuracy. Predictor geometry helps explain available learning directions, while held-out decision quality remains the test of practical benefit.

Bank treasury portfolios must balance yield, liquidity, and interest-rate risk across bonds of different maturities. Static allocation rules are ill-suited to this task: portfolios concentrated in long-duration securities with no dynamic adjust- ment mechanism can accumulate large mark-to-market losses and liquidity stress under rising interest rates, as illustrated by the failure of Silicon Valley Bank in 2023. We develop a tractable simulation-based framework for multi-period bond port- folio optimization under interest-rate risk and proportional transaction costs. Yield-curve dynamics are modeled using the Dynamic Nelson-Siegel parameter- ization with Vector Autoregressive factor dynamics, from which we construct a time-inhomogeneous discrete-state Markov chain approximating the joint yield process across bond maturities. This chain forms the state space of a finite- horizon Markov Decision Process in which the investor maximizes expected terminal wealth subject to proportional rebalancing costs. The optimal portfolio policy is obtained by backward induction. We also quantify the approximation error introduced by truncating the transition kernel, and show that it leaves mean terminal wealth almost unchanged while substantially distorting drawdown and tail statistics.

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.

News may reveal systematic risk, but whether its context enhances the construction of systematic risk factors is still unclear. We seek to test whether utilizing a sentence transformer represents an improvement over techniques such as Latent Dirichlet Allocation (LDA) in the coherence of topic term lists generated from unstructured text data. To test this, the same collection of unstructured text data comprising of 394,661 articles and the same downstream financial portfolio construction pipeline were applied with the text layer differing, including the length of article text each model used and how topic terms were ranked: we benchmark LDA against a frozen sentence transformer with k-means clustering. We find that the sentence transformer branch had higher observed scores both in terms of coherence (measured by NPMI) as well as financial performance (measured by Sharpe), although the available tests do not establish outperformance. Further exploratory specifications such as utilizing spherical clustering and multi-horizon exposures had an observed excess-return Sharpe of 1.03 for the combined model. We believe that there is some promise in applying context-aware techniques on unstructured news text, but stricter tests using only information available at each date and broader datasets may be required to enhance the confidence in the observed performance.

We present an end-to-end deep learning framework for systematic options trading that directly embeds hedging behavior through explicit control of portfolio-level risk exposures. While neural networks trained to optimize risk-adjusted performance have been shown to outperform traditional rules-based strategies, such approaches remain agnostic to the sensitivities of the resulting portfolios with respect to specific underlying risk factors. We propose a general training objective that combines a performance-driven loss with a differentiable risk-sensitivity penalty, enforcing neutrality to selected risk dimensions. Unlike reinforcement learning methods that approximate optimal hedging policies via simulated market dynamics, our framework operates entirely on historical data and jointly optimizes risk-adjusted returns and targeted risk constraints in a single learning problem. We instantiate the framework on static delta-neutral straddle portfolios with the penalty directed at first-order directional exposure, and evaluate two penalty variants – an exposure-normalized penalty and a Greek-ratio drift penalty. Empirical results on Nasdaq 100 equity options demonstrate that appropriately calibrated regularization simultaneously improves out-of-sample risk-adjusted performance relative to an unregularized baseline while reducing realized directional exposure.

We consider a problem of optimal proportional reinsurance-dividend distribution under a Brownian risk model, where both the drift and volatility coefficients are subject to endogenous regime-switching. Dividend payments are subject to fixed transaction costs. The problem is formulated as a two-dimensional stochastic control problem, and we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with nonlocal operator. For almost all parameter configurations, we explicitly characterize the optimal strategy that maximizes the expected total discounted dividends net of transaction costs until ruin. The optimal dividend policy is a two-barrier impulsive strategy, while the optimal reinsurance proportion is given in feedback form. Numerical examples are provided to illustrate the optimality results.

This paper investigates cost-sensitive online window size selection for portfolio management under changing market conditions. Specifically, we propose a two-level framework that constructs portfolios using candidate window sizes and dynamically aggregates them through online learning. By treating candidate window sizes as “experts,” we dynamically update their aggregation weights using turnover-inclusive losses. Moreover, we derive finite-horizon cost-sensitive tracking-regret bounds that account for turnover of the aggregated portfolio, with static regret as a special case. Under bounded losses and cost rates, suitably tuned Fixed Share achieves asymptotically no tracking regret for sublinear switching budgets, with Hedge covering the static case.

The equal-weighted portfolio is a passive, rule-based strategy that has historically been difficult to outperform, delivering higher returns than the capitalization-weighted "market" benchmark across many markets and periods. Stochastic portfolio theory (SPT) reveals that this relative performance is regime dependent, with the equal-weighted portfolio underperforming during periods of increasing market concentration and high correlations, particularly market bubbles. These observations have motivated us to formulate and solve a stochastic control problem in which an investor actively allocates between the equal-weighted and market portfolios. The investor bases their allocation decisions on forecasts made under a flexible stochastic diversity–dispersion (SDD) model. Using a quadratic surrogate for implementation frictions, we characterize the optimal allocation through a linear forward–backward SDE and obtain an explicit "aiming in front of a moving target" representation of the optimal trading rate, in the spirit of Gârleanu and Pedersen. The penalty parameters are calibrated in sample to match the cumulative wealth effect of proportional transaction costs, while out-of-sample performance is evaluated with those costs deducted directly from portfolio wealth. Using historical S&P 500 data, we show that a mean-reverting SDD specification reproduces several empirical features of market diversity and dispersion. In out-of-sample backtests from 1995 to 2024, the resulting strategies deliver higher cumulative net returns than both the equal-weighted and market portfolios, and higher information ratios than the equal-weighted portfolio after 15-basis-point proportional transaction costs.

Language-model agents now run the whole of quantitative factor research: they propose investment factors, backtest them, select the survivors and retire them. We ask which of those jobs an agent should keep. Our answer is governed self-evolution: the agent may propose, and a frozen statistical referee that the agent cannot touch must judge. The referee scores each candidate only on market outcomes revealed after submission, by betting, so its false-discovery guarantee holds at every stopping time for any proposal policy. We cross three proposers (a script, a bandit and a language model) with this referee and with three deliberately leaky ones, in a synthetic world with planted truth, a probe-authoring environment and a ten-year walk-forward on the CSI 500. Who judges sets the number of false admissions: the frozen referee admits 5-11 times fewer sub-threshold factors than the leaky referees under a scripted proposer, and no proposer closes that gap. Who proposes sets the yield: the language model beats the script, matches the bandit, and adds the one capability a bandit lacks, writing its own diagnostic probes. The certificate's price is time: an admitted true factor waits about 500 trading days, and the certified portfolio's Sharpe ratio therefore trails an ungated one. Judging belongs to the procedure; proposing and instrument-making belong to the agent.

We study the infinite-horizon optimal investment and consumption problem in a general class of continuous financial markets, where uncertainty is driven by a continuous non-decreasing stochastic clock representing accumulated variance. This framework encompasses classical Markovian and non-Markovian stochastic volatility models as well as singular realized-variance models in which no spot volatility process exists. We characterize the value process and optimal investment and consumption strategies in terms of a non-linear infinite-horizon backward stochastic differential equation driven jointly by calendar time and the stochastic clock. We develop a general well-posedness theory for this new class of IVC-BSDEs based on the method of sub- and supersolutions, establishing existence, uniqueness, and stability under natural conditions that might be of independent interest beyond the financial application at hand. We are moreover able to identify the sign of the $Z$-component of the solution using Malliavin calculus. We then apply our results to Volterra Heston models with locally integrable kernels, covering both rough and hyper-rough regimes. Exploiting the affine structure of the model, we verify the optimality of the candidate strategies in incomplete markets and obtain an explicit representation of the solution in the complete market case. Owing to the generality of the framework and the weak assumptions imposed on the stochastic clock, our results unify and extend several existing results for optimal investment and consumption, including classical Markovian stochastic volatility models.