Emilio Barucci, Yuheng Lan, Daniele Marazzina
Apr 23, 2026·q-fin.MF·PDF We investigate the optimal execution of contracts that are used in merger\&acquisition deals. We consider cash-settled and physically delivered contracts between a broker and a counterpart. Contracts are linear (total returns swaps), nonlinear (collar contracts) or Asian type (TWAP based contracts). We derive the optimal execution strategy and the optimal fee through indifference utility arguments allowing for linear market effects of trades. We show that linear cash-settled contracts are more expensive and more exposed to manipulation/statistical arbitrages by the broker. Also nonlinear and Asian type contracts are exposed to these phenomena.
Robert Flassig, Emrah Gülay, Daniel Guterding
Apr 21, 2026·q-fin.CP·PDF The Nelson-Siegel-Svensson (NSS) interest rate curve model yields a separable nonlinear least-squares problem whose inner linear block is often ill-conditioned because the basis functions become nearly collinear. We analyze this instability via an exact orthogonal reparametrization of the design matrix. A thin QR decomposition produces orthogonal linear parameters for which, conditional on the nonlinear parameters, the Fisher information matrix is diagonal. We also derive a finite-horizon analytical orthogonalization: on $[0,T]$, the $4\times 4$ continuous Gram matrix has closed-form entries involving exponentials, logarithms, and the exponential integral $E_1$, yielding an explicit horizon-dependent orthogonal NSS basis. Together with Jacobian-rank and profile-likelihood arguments, this representation clarifies the degenerate manifold $λ_1=λ_2$, where the Svensson extension loses two degrees of freedom. Orthogonalization leaves the least-squares fit and uncertainty of the original linear parameters unchanged, but isolates the conditioning structure. When the decay parameters are estimated jointly, the full first-order covariance in orthogonal coordinates admits an explicit Schur-complement form. The approach also yields a scalar identifiability diagnostic through the QR element $R_{44}$ and separates model reduction from numerical instability. Synthetic experiments confirm that orthogonal parametrization eliminates correlations among the linear parameters and keeps their conditional uncertainty uniform. A daily U.S. Treasury study on a reduced fixed 9-tenor grid from 1981 to 2026 shows smoother orthogonal parameter series than classical NSS parameters while the moving QR basis remains nearly constant.
Simon Hochgerner, Jonas Ingmanns, Nicole Kastanek
Apr 20, 2026·q-fin.MF·PDF Up to inflation, the basic cash flow associated to health insurance policies is independent from capital markets. It has therefore been common to calculate the Best Estimate based on a deterministic approach. However, in the light of volatile inflation dynamics in recent years, it has become more popular to use stochastic models for the Best Estimate of health insurance policies. In this article, we show that this stochastic approach is preferable and provide a framework to efficiently evaluate a large stock of health insurance policies. More precisely, we first prove that the Best Estimate of a life-long health insurance policy depends on the choice of model for the interest and inflation rates. That is, the Best Estimate is not uniquely determined by the current nominal and real spot rates used to calibrate these type of models -- even without profit participation or the common practice of limiting premium adjustments. Second, we construct a valuation portfolio for life-long health insurance policies without the common industry practice of limiting the premium adjustments, decomposing the Best Estimate into 1.) deterministic coefficients derived from policy data and 2.) the prices of basis financial instruments that are independent of the individual policy data. Using this decomposition, the policies do not have to be tracked individually along each generated inflation path. This allows a very efficient evaluation of the Best Estimate for a large stock of policies with a stochastic model.
Anastasiia Zbandut, Carolina Goldstein
Apr 19, 2026·q-fin.RM·PDF We derive five tractable credit risk metrics for DeFi lending vault depositors, grounded in a formal three level decomposition of vault risk into mechanical loss channels (Level 1), governance quality (Level 2) and smart contract code integrity (Level 3). For Level 1, we show that six structural features of onchain execution (oracle execution divergence, endogenous recovery, full information run dynamics, timelock constrained governance, oracle manipulation and congestion driven liquidation failure) break canonical TradFi analogies and generate depositor loss channels absent from standard credit frameworks. Vault credit risk metrics translate these channels into measurable risk components which are aggregated into a vault credit score. The empirical contribution is an implementable estimation architecture for credit risk metrics, including required onchain data, identification strategies for core parameters, partial identification bounds and a coherent stress scenario methodology. The results have direct implications for vault risk management and for minimum transparency standards necessary for depositor risk assessment.
Onésime Hounkpe, Dena Firoozi, Shuang Gao
We propose a decomposition method for solving a general class of linear-quadratic (LQ) McKean-Vlasov control problems involving conditional expectations and random coefficients, where the system dynamics are driven by two independent Wiener processes. Unlike existing approaches in the literature for these problems, such as the extended stochastic maximum principle and the extended dynamic programming methods, which often involve additional technical complexities and sometimes impose restrictive conditions on control inputs, our approach decomposes the original McKean-Vlasov control problem into two decoupled stochastic optimal control problems, one of which has a constrained admissible control set. These auxiliary problems can be solved using classical methods. We establish an equivalence between the well-posedness and solvability of the auxiliary problems and those of the original problem, and show that the sum of the optimal controls of the auxiliary problems yields the optimal control of the original problem. Moreover, by applying a variational method, we characterize the optimal solution to the McKean-Vlasov control problem via two decoupled sets of (non-McKean-Vlasov) linear forward-backward stochastic differential equations, each corresponding to one of the auxiliary problems. Finally, we show that standard dynamic programming can also be applied to solve the resulting auxiliary problems.
Huisheng Wang, H. Vicky Zhao
Apr 13, 2026·q-fin.MF·PDF Herding, where investors imitate others' decisions rather than relying on their own analysis, is a prevalent phenomenon in financial markets. Excessive herding distorts rational decisions, amplifies volatility, and can be exploited by manipulators to harm the market. Traditional regulatory tools, such as information disclosure and transaction restrictions, are often imprecise and lack theoretical guarantees for effectiveness. This calls for a quantitative approach to regulating herding. We propose a regulator-leader-follower trilateral game framework based on optimal control theory to study the complex dynamics among them. The leader makes rational decisions, the follower maximizes utility while aligning with the leader's decisions, whereas the regulator designs a mechanism to maximize social welfare and minimize regulatory cost. We derive the follower's decisions and the regulator's mechanisms, theoretically analyze the impact of regulation on decisions, and investigate effective mechanisms to improve social welfare.
Takanori Adachi
Apr 12, 2026·q-fin.MF·PDF We introduce a new perspective on arbitrage based on global loop effects in filtered market systems, providing a conceptual extension of classical arbitrage theory beyond local consistency conditions. Given a filtration modeled as a contravariant functor $F : \mathcal{T}^{op} \to \mathrm{Prob}$, we consider the associated conditional expectation functor $\mathcal{E} \circ F$ and show that it induces a canonical multiplicative distortion $dF(i) := (\mathcal{E} \circ F)(i)(1)$, which measures the failure of constant functions to be preserved under non-measure-preserving transitions. We define the holonomy of $dF$ along loops in $\mathcal{T}$ and interpret non-trivial holonomy as a global inconsistency that is invisible at the level of individual transitions. This leads to a notion of Aharonov--Bohm (AB) arbitrage, in which arbitrage arises from loop effects rather than local price discrepancies. We further show that, under suitable admissibility conditions, non-trivial holonomy can be converted into a predictable self-financing trading strategy. This establishes a connection between cohomological structures and economically realizable arbitrage, highlighting the role of global invariants in the structure of financial markets.
Seongjin Kim, Jin Hyuk Choi
Apr 11, 2026·q-fin.TR·PDF We develop a multi-period Kyle-type model that incorporates both mandatory disclosure of informed trades and imperfect competition among market makers. We prove the existence and uniqueness of a linear equilibrium and show that the liquidity-enhancing effect of disclosure is fundamentally linked to the degree of market-making competition. Disclosure lowers trading costs by reducing price impact, and its marginal benefit is strictly larger when competition is weak. We empirically validate this prediction using the 2002 Sarbanes-Oxley Act disclosure reform as a natural experiment. A difference-in-differences analysis of U.S. equities confirms that the spread reduction following enhanced disclosure is significantly larger for stocks with fewer active market makers.
Alec Kercheval, Ololade Sowunmi
Apr 11, 2026·q-fin.MF·PDF We study the long-only minimum variance (LOMV) portfolio under a one-factor covariance model with asset betas of arbitrary sign. We provide an explicit solution in terms of the set of active (positive weight) assets, and provide an explicit and computable characterization of the active set. As a corollary we resolve an open question of \citet{qi2021} concerning the extension to mixed-sign betas. In the high-dimensional regime $p \to \infty$ where the betas are drawn from a distribution with cdf $F$, we prove that the proportion of active assets (the active ratio) in the LOMV portfolio converges in almost all cases to $F(β^{*})$, where $β^* \geq 0$ is the root of an explicit integral equation determined by $F$. This is a variation of a result first appearing in \citet{bernstein2025}. In particular, when $F$ is continuous and all betas are positive ($F(0)=0$), the active ratio converges to zero. When $F(0) >0$ is small, under mild moment conditions and concentration bounds we establish the convergence rate $F(β^*)=O(F(0)^{1/3})$ as $F(0) \to 0$.
Matteo Buttarazzi
Apr 10, 2026·q-fin.MF·PDF In this paper, we derive explicit closed-form solutions for the value function and the associated optimal stopping boundaries in an optimal annuitization problem under a mortality shock. We consider an individual whose retirement wealth is invested in a financial fund following the dynamics of a geometric Brownian motion and has the option at any time to irreversibly convert their wealth into a life annuity. The individual faces a sudden, permanent health deterioration occurring at a random, exponentially distributed time, and the annuitization decision is modelled as an optimal stopping problem across two health states. Our analytical expressions characterise both the value function and the optimal timing of annuitization. The results provide clear economic intuition: the optimal strategy is governed by the critical interplay between the relative attractiveness of the annuity (money's worth), the financial returns from the investment fund, and bequest motives across different health states. A numerical analysis compares the optimal annuitization strategy of an individual facing a health shock against a benchmark case with constant mortality, highlighting how the likelihood and severity of a health shock significantly alter optimal annuitization behaviour.
Asmerilda Hitaj, Elisa Mastrogiacomo, Ilaria Peri, Marcelo Righi
This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio, RAROC, or Omega-that express reward per unit of risk, ranking metrics assign each position a performance level rather than a normalized return. Relying on monotonicity and a new property called cash-quasiconcavity, we derive representation results linking ranking metrics to families of acceptance sets and risk measures, extending the theory of acceptability indices. Classical ratios arise as special cases, while new examples-based on expected-loss, Lambda-quantile, and bibliometric indices-illustrate the framework's flexibility. Empirical applications to portfolio ranking and climate-risk insurance demonstrate its practical relevance.
Daniel Bloch
This paper introduces a novel generative framework for synthesising forward-looking, càdlàg stochastic trajectories that are sequentially consistent with time-evolving path-law proxies, thereby incorporating anticipated structural breaks, regime shifts, and non-autonomous dynamics. By framing path synthesis as a sequential matching problem on restricted Skorokhod manifolds, we develop the \textit{Anticipatory Neural Jump-Diffusion} (ANJD) flow, a generative mechanism that effectively inverts the time-extended Marcus-sense signature. Central to this approach is the Anticipatory Variance-Normalised Signature Geometry (AVNSG), a time-evolving precision operator that performs dynamic spectral whitening on the signature manifold to ensure contractivity during volatile regime shifts and discrete aleatoric shocks. We provide a rigorous theoretical analysis demonstrating that the joint generative flow constitutes an infinitesimal steepest descent direction for the Maximum Mean Discrepancy functional relative to a moving target proxy. Furthermore, we establish statistical generalisation bounds within the restricted path-space and analyse the Rademacher complexity of the whitened signature functionals to characterise the expressive power of the model under heavy-tailed innovations. The framework is implemented via a scalable numerical scheme involving Nyström-compressed score-matching and an anticipatory hybrid Euler-Maruyama-Marcus integration scheme. Our results demonstrate that the proposed method captures the non-commutative moments and high-order stochastic texture of complex, discontinuous path-laws with high computational efficiency.
Daniel Bloch
This paper introduces Anticipatory Reinforcement Learning (ARL), a novel framework designed to bridge the gap between non-Markovian decision processes and classical reinforcement learning architectures, specifically under the constraint of a single observed trajectory. In environments characterised by jump-diffusions and structural breaks, traditional state-based methods often fail to capture the essential path-dependent geometry required for accurate foresight. We resolve this by lifting the state space into a signature-augmented manifold, where the history of the process is embedded as a dynamical coordinate. By utilising a self-consistent field approach, the agent maintains an anticipated proxy of the future path-law, allowing for a deterministic evaluation of expected returns. This transition from stochastic branching to a single-pass linear evaluation significantly reduces computational complexity and variance. We prove that this framework preserves fundamental contraction properties and ensures stable generalisation even in the presence of heavy-tailed noise. Our results demonstrate that by grounding reinforcement learning in the topological features of path-space, agents can achieve proactive risk management and superior policy stability in highly volatile, continuous-time environments.
Xinyu Chen, Zuo Quan Xu
This paper studies an $α$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market returns. The $α$-robust criterion interpolates between worst-case ($α=0$) and best-case ($α=1$) evaluations, generalizing both extremes through a continuous ambiguity attitude parameter. For weighted exponential utilities, we establish via rearrangement inequalities and comonotonicity theory that the $α$-robust risk measure is law-invariant, depending only on marginal distributions. This transforms the dynamic stochastic control problem into a concave static quantile optimization over a convex domain. We derive optimality conditions via calculus of variations and characterize the optimal quantile as the solution to a two-dimensional first-order ordinary differential equation system, which is a system of variational inequalities with mixed boundary conditions, enabling numerical solution. Our framework naturally accommodates additional risk constraints such as Value-at-Risk and Expected Shortfall. Numerical experiments reveal how ambiguity attitude, market conditions, and claim characteristics interact to shape optimal payoffs.
Chonghu Guan, Zuo Quan Xu
We consider an optimal dividend payout problem for an insurance company whose surplus follows the classical Cramér-Lundberg model. The dividend rate is subject to a ratcheting constraint (i.e., it must be nondecreasing over time), and the company may inject capital at a proportional cost to avoid ruin. This problem gives rise to a stochastic control problem with a self-path-dependent control constraint, costly capital injections, and jump-diffusion dynamics. The associated Hamilton-Jacobi-Bellman (HJB) equation is a partial integro-differential variational inequality featuring both a nonlocal integral term and a gradient constraint. We develop a systematic probabilistic and PDE-based approach to solve this HJB equation. By discretizing the space of admissible dividend rates, we construct a sequence of approximating regime-switching systems of ordinary integro-differential equations. Through careful a priori estimates and a limiting argument, we prove the existence and uniqueness of a \emph{strong solution} in a suitable space. This regularity result is fundamental: it allows us to characterize the optimal dividend policy via a switching free boundary and to construct an explicit optimal feedback control strategy. To the best of our knowledge, this is the first complete solution -- comprising both the value function and an implementable optimal strategy -- for a dividend ratcheting problem with capital injection under the Cramér-Lundberg model. Our work advances the mathematical theory of optimal stochastic control beyond the standard viscosity solution framework, providing a rigorous foundation for dividend policy design in economics.
Li Lin
Classical asset pricing relies on the risk-neutral measure $Q$ for valuation, yet its economic interpretation is typically anchored in a physical measure $P$. This creates an inherent asymmetry: pricing is governed by $Q$, while meaning resides in $P$, making it difficult to provide a unified account of asset pricing within a single conceptual framework. This paper proposes an alternative perspective based on information geometry, termed Financial Relativity. Its central principle is the relativity of probabilistic reference frames: $P$ and $Q$ have no intrinsic hierarchy, but instead represent geometric structures induced by different informational constraints. Terminal structural information shapes probability geometry, which in turn governs how information is expressed in prices. Within this framework, the risk-neutral measure is reinterpreted as a posterior probability geometry. Asset prices are characterized as geometric projections of terminal payoffs onto information subspaces, and their dynamics reflect the progressive manifestation of structural information under evolving geometry. We develop both discrete and continuous financial field equations to describe the formation of probability geometry and derive geodesic price dynamics in which volatility arises endogenously from posterior uncertainty. The framework provides a unified explanation for price fluctuations, event-driven behavior, and risk premia, and yields testable implications, including structural links between volatility and posterior variance and measures of price informational efficiency. By integrating structural information, probability measures, and price dynamics within a single geometric framework, the paper offers a coherent, extensible, and empirically tractable reinterpretation of asset pricing.
Alessandro Doldi, Marco Frittelli, Marco Maggis
Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive a necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents' preferences and collective pricing measures. The framework applies to both continuous- and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent's indirect utility.
Yun Zhao, Alex S. L. Tse, Harry Zheng
We study a speculative trading problem within the exploratory reinforcement learning (RL) framework of Wang et al. [2020]. The problem is formulated as a sequential optimal stopping problem over entry and exit times under general utility function and price process. We first consider a relaxed version of the problem in which the stopping times are modeled by the jump times of Cox processes driven by bounded, non-randomized intensity controls. Under the exploratory formulation, the agent's randomized control is characterized via the probability measure over the jump intensities, and their objective function is regularized by Shannon's differential entropy. This yields a system of the exploratory HJB equations and Gibbs distributions in closed-form as the optimal policy. Error estimates and convergence of the RL objective to the value function of the original problem are established. Finally, an RL algorithm is designed, and its implementation is showcased in a pairs-trading application.
Emmanuel Gnabeyeu
We investigate the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of fake stationary affine Volterra models. In this non-Markovian and non-semimartingale market framework with unbounded random coefficients, the classical stochastic control approach cannot be directly applied to the associated optimization task. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). The optimal feedback control is characterized by means of this equation, whose explicit solutions is derived in terms of multi-dimensional Riccati-Volterra equations. Specifically, we obtain analytical closed-form expressions for the optimal portfolio policies as well as the mean-variance efficient frontier, both of which depend on the solution to the associated multivariate Riccati-Volterra system. To illustrate our results, numerical experiments based on a two dimensional fake stationary rough Heston model highlight the impact of rough volatilities and stochastic correlations on the optimal Markowitz strategies.
Julio Backhoff, Mathias Beiglböck, Giorgia Bifronte, Armand Ley
We investigate the martingale Schrödinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to arbitrary dimension and admits several equivalent characterizations. In particular, we identify its continuous-time counterpart as the continuous martingale with prescribed marginals that minimizes a weighted quadratic energy measuring the deviation from Brownian motion. In the irreducible case, we prove that this continuous martingale Schrödinger bridge coincides with the Föllmer martingale, that is, with the Doob martingale associated to a suitable Föllmer process. More generally, we relate the martingale Schrödinger bridge to a variational problem over base measures and to the dual formulation of the corresponding weak optimal transport problem, thereby clarifying its connection with the classical Schrödinger bridge.