Papers

In this paper we investigate the information content of the lower part of the spectrum of financial correlation matrices, as a source of information on market synchronization. In a financial context, a classical application of Principal Component Analysis and Random Matrix Theory identifies the largest eigenvalues as indicators of dominant market factors and synchronization patterns. We complement this perspective by showing that the smallest eigenvalues also contain relevant information about the effective structure of financial markets. The paper presents the methodological proposal and validates its effectiveness through comprehensive real data experiments in both descriptive and predictive settings.

Cryptocurrency exchange-traded products (ETPs) listed on European exchanges provide a regulated environment for studying intraday market anomalies. We study four Bitcoin and Ethereum ETPs traded on Xetra and Nasdaq Stockholm over the period January 2024 - December 2025 using one-minute bars. As a benchmark, we adopt an extreme value theory approach in which anomalous bars are defined as returns falling below a threshold estimated by fitting a generalised Pareto distribution to left-tail exceedances. We then propose three new binary anomaly indicators. The first, a cross-venue divergence anomaly, identifies venue-specific price divergence between the two exchanges. The second is a no-recovery anomaly that identifies extreme price drops followed by little or no recovery over the next ten active bars. The third is a momentum-reversal anomaly that identifies extreme price drops following positive short-term momentum. Although each anomaly type represents fewer than 1% of one-minute bars, statistical analysis using Mann-Whitney U tests shows that anomaly observations exhibit significantly higher effective spreads, higher values of liquidity-related ratios, and more pronounced order-flow imbalances than non-anomalous bars. Furthermore, employing an out-of-sample prediction methodology with four classifiers - random forest, logistic regression, extreme gradient boosting, and light gradient boosting machine - shows that all four anomaly types are predictable one bar ahead, with AUC-ROC values of up to 0.82. Permutation importance indicates that short-term volatility and drawdown measures are generally more useful for prediction than microstructure variables.

Completely monotonic inverse marginal (CMIM) utilities, introduced in [MSZ24], constitute a tractable class of preferences that includes many of the most important utility functions used in mathematical finance, such as power and exponential utilities. In stochastically dominant markets, their Bernstein representation induces a hidden linear structure in the dual optimization problem that serves as the foundation for the present analysis. In this paper, we investigate the sensitivity of optimal investment with respect to perturbations of investor preferences within the CMIM class. Exploiting Bernstein's representation theorem, we show that, under stochastic dominance, affine perturbations of Bernstein measures induce an affine representation of the dual value function. As a result, the dependence of the optimization problem on preferences can be analyzed through a scalar budget equation, allowing us to prove analyticity of the associated Lagrange multiplier with respect to the perturbation parameter and to derive convergent analytic expansions of arbitrary order for the primal value function and the optimal terminal wealth, with explicit recursive formulas expressed through Bell polynomials.

In this paper, we consider an optimal stopping problem with infinite horizon, non-negative pay-offs and non-linear evaluations $\rho_{S,\tau}$ indexed by two indices: $S$ and $\tau$, where $S$ is the time of evaluation and $\tau$ is the time when the pay-off is revealed. The agent's stopping strategies are constrained to be in the set of so-called Bermudan stopping times $\Theta$. Under suitable assumptions on the non-linear evaluations $\rho$ and on the pay-off, we show that a dynamic programming principle holds in this framework. We investigate the existence of $\varepsilon$-optimal stopping times, as well as the existence of optimal stopping times. We show that an $\varepsilon$-optimal stopping time exists. We also prove that the first time when the value family hits the pay-off is optimal if and only if it is finite. We also provide Doob's type convergence for non-negative \emph{$(\Theta, \rho)$}-supermartingales in the case where $\rho_{S,\tau}=\rho_S$ depends on the first index only. We provide an example from BSDEs with infinite horizon.

The paper places the Samuelson–Merton “util-prob” construction and preference-based state-price interpretation inside a continuous-time equivalent-martingale-measure framework. The contribution is not the existence of a marginal-utility pricing kernel, but a compensated stochastic-exponential representation of the “util-prob” density. Behavioral weighting by marginal utility becomes an equivalent martingale measure only after the drift generated by risk aversion and prudence is compensated. Under positivity, integrability, normalization, and martingale conditions, the behavioral density is generated by the Brownian kernel $-A_t\sigma_t$, where $A_t$ is Arrow–Pratt risk attitude and $\sigma_t$ is state volatility. The required compensator identifies the finite-variation term that must be removed before marginal-utility weighting defines a true martingale density. The framework preserves put–call parity under a common admissible kernel and yields a Cox–Ross risk-premium identity linking option and underlying premia through volatility exposures. Empirically, the paper maps option-implied and physical densities into a signed Arrow–Pratt decomposition, with positive curvature interpreted as risk aversion and negative curvature as risk-seeking or speculative tilt. In a panel of liquid index ETF and single-name options, arbitrage-penalized EBMM has lower pooled holdout squared-error loss than arbitrage-penalized SVI when both models receive the same total-variance positivity and butterfly-density penalties, although slice-level results remain mixed. The exercise is best read as a density-ratio admissibility test rather than a replacement for production volatility-surface estimation.

Hawkes-based microstructural foundations for rough volatility, leverage, and rough Heston-type limits were developed by El Euch et al. (2018, Finance Stoch., 22(2), 241–280) and connected to the affine rough Heston framework of El Euch and Rosenbaum (2019, Math. Finance, 29(1), 3–38). The rough Hawkes–Heston model with common price–volatility jumps of Bondi et al. (2024, Math. Finance, 34(4), 1197–1241) extends this framework by adding state-dependent common jumps to rough affine volatility. We provide a microstructural foundation for its variance and common-jump mechanism by constructing a Poisson-embedded marked Hawkes order-flow model. Ordinary arrivals generate rough continuous volatility and leverage through a nearly unstable heavy-tailed Hawkes mechanism, while rare marked arrivals represent common shock events that produce simultaneous price jumps and volatility excitation. Under the nearly unstable scaling and the reduced-form admissibility conditions, the complete rescaled price/variance/jump system converges along the full sequence to the unique complete canonical rough Hawkes–Heston weak solution. The Hawkes renewal structure yields a Mittag–Leffler Volterra representation, which is then rewritten in Riemann–Liouville fractional form. The limiting coefficients are expressed explicitly in terms of the microscopic parameters. The construction provides a microstructural foundation for the variance and common-jump mechanism of the rough Hawkes–Heston model. Numerical experiments illustrate the convergence of our microstructural foundation to the rough Hawkes-Heston model.

We consider a market maker who can only obtain and dispose of inventory by responding to a sequence of sealed-bid enquiries, and whose customers arrive with imbalanced intent: sellers more often than buyers, or the reverse. Under the assumption that the best competing response is exponentially distributed around a commonly discerned fair price, we observe a symmetry in the steady state solution that compresses the imbalanced problem onto the perfectly balanced one. Order imbalance is absorbed, exactly, by a translation of the market maker's skew, a widening of her quotes, and a multiplication of her effective cost of carry. The adjustment is simple even though the solution it adjusts is not, and it involves no free parameter beyond the observable market width. The exponential assumption is needed only locally, at the quotes actually made, and the width that enters is the locally observed one. Among the consequences: a market maker with zero inventory should still skew; skew responds to imbalance at first order whereas width responds only at second order; and the popular "constant width, linear skew" heuristic is recovered as the small-skew solution in the special case of balanced flow and quadratic holding cost.

We study Lambda-quantiles, a generalisation of classical quantiles in which the constant probability level $\lambda \in [0,1]$ is replaced by a functional parameter $\Lambda \colon \mathbb{R} \to [0,1]$. We consider the general case of non-monotone $\Lambda$, which arises naturally if closure properties of the class of corresponding Lambda-quantiles with respect to inf-aggregation or with respect to mixtures are required. As preliminary results, we characterise finiteness, constancy, and what we call the attainment property known from classical quantiles. We then consider the problem of reconstructing $\Lambda$ from the values of $\Lambda$-quantiles on a suitable family of simple distributions, showing its identifiability under mild assumptions. Next, we substantially refine several results obtained in the literature on weak upper and lower semicontinuity and on the property of convexity of the level sets with respect to mixtures, obtaining in both cases almost complete characterisations without any monotonicity assumption. We then move to the case in which $\Lambda$ has bounded variation, which enables us to prove a mixture representation result: any such $\Lambda$-quantile can be rewritten as a Lambda-quantile with an increasing functional parameter, evaluated at a mixture of the original distribution with a fixed reference distribution at a fixed weight, thus reducing the complexity of the parameter from bounded variation to monotone. Finally, we introduce and study the notion of the ordinal covariance group of a risk measure, showing that in the case of a $\Lambda$-quantile it coincides with the compositional invariance group of $\Lambda$ and with a certain group of measure-preserving transformations of the signed measure associated with $\Lambda$.

Neural and numerical policy solvers can produce feasible controls even when the optimal rule and its binding constraints are unavailable. A primal-dual bracket certifies value loss, but it does not locate the optimal policy or explain which constraints genuinely bind. We show that, on the same declared simulation grid, one bracket can support both conclusions. For polyhedral controls, an exact conditional budget identity rewrites the residual as a pathwise nonnegative terminal Fenchel defect plus date-by-constraint complementary-slackness terms. A canonical Doob compensation removes the budget martingale that obscures small residuals. Bellman-primitive curvature conditions then yield an occupancy-weighted policy region with the sharp O(sqrt(G)) radius, while a paired constraint relaxation lower-bounds the optimal multiplier and certifies a binding face. A finite-sample resolution theorem quantifies the path budget needed to certify a target policy tolerance or face. Locked one-asset and two-asset audits cover every external policy error and make no false face declaration. An exact-wrapper stress test remains tight through 50 assets, while a separate state-dependent pilot identifies learned-dual tightness as the high-dimensional bottleneck. Reference solutions enter only after certification.

This article studies a dynamic corporate risk management problem by considering the decision-making of risk-averse managers who exert costly effort and select project risk. We study how a Value-at-Risk (VaR) constraint affects managerial decisions and the distribution of firm value when the manager's objective is non-concave with a fixed salary and options. By the concavification technique, we analyze the optimal terminal firm value on the concave envelope of the objective function. Applying the quantile formulation and the martingale approach, we can derive explicit solutions for optimal effort, terminal firm value, and project choice. The optimal terminal firm value can be divided into nine cases by carefully discussing the choices of VaR floor and tail probability. Compared with the benchmark case, we find that a VaR manager will smooth terminal firm value across states, reducing it in good states while supporting it in adverse states. Moreover, a VaR requirement generally improves downside protection and reduces bankruptcy probability when the VaR floor is low or moderate. However, when the VaR floor is sufficiently high, it can increase bankruptcy probability and induce gambling-for-recovery behavior in adverse states. Our sensitivity analysis indicates that greater managerial effort uniformly improves firm value. Moreover, more incentive options make managers more responsible, leading to a smoother terminal firm value across states. In contrast, a high fixed salary makes the manager less responsible and ultimately causes a more dispersed firm value.

We study utility maximization for high-frequency trading in fractional Brownian motion models. We first consider exponential utility in the discretized arithmetic model. Using spectral methods for stationary Gaussian sequences, we derive the asymptotic growth rate of the optimal certainty equivalent and the scaling limit of the optimal positions. We then consider power and logarithmic utility in a positive-price model with positive wealth and investment fractions in $[0,1]$. In this case, the logarithm of the optimal certainty equivalent grows at rate $n^{1-H}$ for $H\neq1/2$, with a coefficient determined by the one-sided prediction error of fractional Gaussian noise. We also give a simple binary strategy which attains this leading rate, without claiming exact finite-horizon optimality.

The transmission of financial distress depends on the structure of exposures, the distribution of institutional buffers, and the duration of stress. We develop a dynamic model in which losses flow through weighted directed networks while counterparties are distressed, with recovery and repeated threshold crossings incorporated into the same system. A representation with \(K\) exposure factors closes the \(N\)-institution dynamics through \(K\) feedback coordinates, preserving heterogeneous sender and receiver roles. For bounded Lipschitz losses, Wasserstein stability and aligned \(L^1\) kernel estimates connect finite populations, factor models, and directed-kernel limits, with separate bounds for sampling and exposure approximation. For the hard threshold, every bounded nonnegative kernel admits a greatest cumulative-distress solution selected by vanishing positive-side regularization. The mass of institutions near the threshold governs stability: an Osgood condition along one reference path yields uniqueness, quantitative perturbation bounds, and convergence under sampled latent labels. Rank-one examples establish sharpness among uniqueness criteria based on threshold-layer mass, and a branchwise condition verifies the regularity directly from the initial profile and kernel. Numerical experiments examine how network structure and threshold concentration affect the dynamics. An application to disclosed EBA sovereign holdings constructs common-exposure factors and quantifies sensitivity to portfolio perturbations.

This paper develops a unified mathematical theory of implied, local, and learned volatility surfaces. Total variance $w_t(k,\tau)=\tau\sigma_t^2(k,\tau)$ is an infinite-dimensional state constrained by positivity, calendar monotonicity, and the butterfly differential inequality. We establish the topology and tangent geometry of this arbitrage set and prove that a nondegenerate Gaussian shock at an active constraint exits with probability tending to one half. Exact invariance therefore requires tangency, reflection, or confinement to an arbitrage-free manifold. We separate this static invariance problem from dynamic no-arbitrage, derive the Musiela maturity-transport identity, and identify the additional fixed-contract martingale restriction. We formulate Hilbert-space dynamics, prove an exact modal reduction with closed-form truncation error, derive Karhunen–Loève factors, identify the portfolio derivative as a vega field, and obtain the covariance-optimal hedge $\alpha^\ast=(H^\ast C H)^{-1}H^\ast C\nu$. The local-volatility chart completes the geometry: Dupire local variance is the ratio $a=\partial_\tau w/g[w]$ of the calendar and butterfly constraint functionals. Neural operators provide arbitrage-free universal approximation through simplex and cone heads. Normalizing-flow maps then add tractable conditional densities: we derive exact change-of-variables formulae for exponential local-variance flows and invertible stick-breaking price-simplex flows, while stating the quasi-invariance conditions required in genuine function space. Finally, fading-signature fields encode surface history and yield autonomous finite-dimensional controlled dynamics. The result is one framework for representation, dynamics, arbitrage, dimension reduction, likelihood-based learning, simulation, and hedging, together with a falsifiable empirical protocol.

Financial sentiment classifiers are commonly evaluated against human labels, but strong linguistic performance does not necessarily imply economically useful return predictability. This study separates these questions through two experiments. First, we construct a unified three-class benchmark from five financial text datasets and compare TF–IDF Naive Bayes, off-the-shelf FinBERT and Financial-RoBERTa encoders, zero-shot Qwen2.5-7B, and QLoRA-adapted Qwen2.5-7B, LLaMA3-8B, and Mistral-7B models. Mistral-7B achieves the best test accuracy (0.8840) and macro-F1 (0.8771), while QLoRA raises Qwen2.5's macro-F1 from 0.7274 to 0.8615. An inverse-frequency class-weighted loss does not improve Qwen2.5. Second, we evaluate economic validity on a temporally separate 2019 Benzinga sample containing 10,637 unique headlines and 13,115 headline–stock observations for a fixed S&P~100 universe. Model probabilities are converted into continuous sentiment scores, aggregated by stock and signal date, and aligned with next-session returns over one-, two-, three-, and five-day horizons. All seven downstream models produce positive but small mean rank information coefficients at the one-day horizon; the largest is 0.0143 for FinBERT. None of the 28 model–horizon tests remains significant after Newey–West inference and false-discovery-rate correction. Portfolio results likewise fail to establish a robust advantage for the best-performing classifiers. The findings show that QLoRA is effective for financial sentiment adaptation, while also documenting a clear gap between classification accuracy and tradable cross-sectional signals.

Fractional Brownian motion (fBm) exhibits attractive features for financial modeling, including long-range dependence, path roughness, and anomalous diffusion. However, its non-semimartingale nature precludes the use of conventional no-arbitrage approaches to option pricing. We address this limitation by introducing a time-changed fBm, obtained by evaluating fBm at stochastic gamma activity time, where activity time represents cumulative executed trading time. The resulting process retains the defining properties of fBm while recovering the semimartingale structure. Building on this construction, we develop the fractional Variance Gamma (fVG) model and propose a generalized method of moments (GMM) estimation procedure for option pricing. An empirical analysis of the S&P 500 yields an estimated Hurst exponent of approximately 0.45, consistent with mildly sublinear temporal scaling of return moments.

We revisit the “collapse to the mean” phenomenon, which refers to mild structural conditions, such as local linearity, that force a law-invariant functional $\ph$ defined on finite-mean random variables to depend solely on the expectation of its argument $X$, and not on any other distributional feature. Starting from a concise characterisation of the convex order, our simplified approach unifies and extends existing results without assuming the functional to be convex or monotone in the almost-sure order, and clarifies the conceptual foundations of the “collapse to the mean" phenomenon. In addition, we establish a new “dual collapse” result for quasi-star-shaped functionals.

Automated market makers (AMMs) are typically interpreted and evaluated as decentralized exchanges. Herein, we take the perspective envisioned by Balancer that an AMM can also be viewed as a portfolio technology that programmatically enforces an economic mandate. In particular, we follow the geometric mean market maker (G3M) invariant employed by that protocol in order to enforce a target-weighted portfolio. We introduce a multi-asset fee structure to the G3M under which competitive arbitrage implements a band-rebalancing strategy with mis-weighting bounded ex ante, allowing compliance with the mandate to be verified directly from the pool's observable holdings. We then compare simulated G3M portfolios against the realized performance of VBIAX, EQL, and EDOW on annualized returns and tracking error against the portfolio mandate. Across these historical case studies, and using arbitrage-only order flow, the G3M is found to outperform the incumbent funds in both metrics for certain fee ranges.

We introduce a framework for preference-robust decision making when preferences over risk are modelled through generalised distortion risk measures. Unlike distributional robustness, our approach addresses ambiguity in the risk functional itself. We construct ambiguity sets on distortion (weight) functions using the Wasserstein distance and Bregman divergences, and derive closed-form expressions for the worst- and best-case distortion risk measures. We further extend the framework to rank-dependent utility, yielding preference-robust behavioural models. In particular, rank-dependent utility appears as a robustification of the expected utility model, yielding a novel way to address the Allais paradox.

We formulate an over-the-counter (OTC) market-making problem in which request-for-quote (RFQ) arrivals are modelled by general Hawkes kernels and fills are controlled thinnings of the exogenous request flow. The modelling choice is motivated by spot-FX RFQ data: after filtering and transforming to seasonality-adjusted RFQ activity time, two-way activity in major currency pairs exhibits large fitted branching ratios and multi-scale persistence. For general Hawkes kernels the control problem is path-dependent: the relevant state contains the order-flow history, or equivalently the forward curve of conditional future RFQ intensities. Exact Markovian lifting is available for exponential kernels, but it becomes high-dimensional for mixtures of exponentials and impractical for long-memory kernels. We therefore develop a hierarchy of Volterra-Riccati approximations. The first level replaces random future request flow by its conditional Volterra forecast; the second adds a covariance correction for intensity uncertainty; the third updates the quote rule with the realized Hawkes memory, or equivalently with the post-request conditional forecast curve. The approximation hierarchy is validated in an exponential Hawkes benchmark, where the exact lifted HJB can be solved numerically. The state-feedback Volterra-Riccati policy closely tracks the exact benchmark, especially in directional regimes, while a memory-free Poisson policy suffers substantial regret. We then apply the same state-feedback rule to a power-law-like RFQ memory model. A directional RFQ burst changes the conditional forecast of future flow and is converted by the continuation-value shadow price into a persistent quote skew. The resulting endogenous OTC quote impact inherits the long-memory decay of the RFQ forecast response and improves inventory and P&L risk control relative to a no-conditioning Poisson benchmark.

We develop a unified modeling framework that connects two distinct types of bubbles defined in the literature: the rational bubbles (aka P-bubbles), and the local martingale bubbles (aka Q-bubbles). We show that the local martingale bubble model includes the classical rational bubble as a special case. We relate both types of bubbles to an equity's risk premium via a novel decomposition.