数理金融

Starting from the classic result of Wentzell, we derive a conditional forward equation and an associated stochastic Dupire PDE for a local-stochastic-volatility model (LSV). As an application, we obtain a density-weighted Rao--Blackwell…

We study a continuous-time portfolio optimization problem in which an investor is evaluated relative to a non-replicable benchmark and seeks to control the persistence of benchmark-relative underperformance. We introduce a…

Electronic over-the-counter (OTC) liquidity provision is increasingly shaped not only by the price of the next quote, but also by a dealer's accumulated standing with clients and platforms. We develop a stochastic-control model in which…

We study optimal portfolio and consumption in a regime-switching multi-name credit market with default contagion. Defaults generate portfolio losses and alter the intensities of surviving securities. Under Cobb--Douglas utility, homogeneity…

In this note, we study distortion risk measures of step-weighted distribution.

Assuming that the asset price $X$ follows a constant elasticity of variance process, this paper studies the optimal prediction problem $\inf_{0\leq \tau\leq T}\mathbb{E}|X_\tau-\ell|$, where the infimum is taken over stopping times $\tau$…

This paper proposes a stochastic discount factor (SDF) scaled by time-varying volatility. By utilizing prices and market data implied solely from S\&P 500 options, the proposed framework recovers a stable, non-monotonic SDF that captures…

Uniformly weighted divergence preferences (UWDP) introduced in Maccheroni et al. (2006) are an important class of risk-averse preferences that contain as a special case the monotone mean--variance utility. UWDP are characterised by the…

Financial markets are hard to predict, not because price moves are purely random, but because structure is strategic, capacity-constrained, and computationally difficult. Classical information theory measures uncertainty, dependence, and…

We consider a class of partial-information portfolio optimization problems in which the drift of a risky asset is driven by two latent stochastic factors evolving at distinct time scales. We show that the filtered estimate of the latent…

Tail-risk management is not only an instrument-selection problem. It is an allocation problem across loss mechanisms: abrupt crash states, volatility repricing, and persistent drawdowns require different forms of protection. This paper…

Financial resilience concerns the rate at which a position recovers, or further deteriorates, in response to adverse conditions. As a first step, Laeven, Ferrari, Rosazza Gianin, and Zullino (arXiv:2505.07502) introduced the resilience…

This paper studies the recovery of uncertainty from dynamic sublinear valuation rules. A robust valuation assigns each payoff its worst-case expected value across plausible models under uncertainty and induces a dynamic sublinear valuation…

The Fundamental Theorem of Asset Pricing states that a market is free of arbitrage exactly when it admits an equivalent martingale measure. We formalize it in Lean 4 over Mathlib in three settings: a finite-state market over a finite…

We study the variance-optimal hedging of European contingent claims written on forwards. We assume that the dynamics of the underlying forward curves follow a Heath--Jarrow--Morton--Musiela stochastic partial differential equation modulated…

Modern resolution and prudential regimes increasingly wind up a distressed firm not at a single hard threshold but through a graduated, state-dependent process. We study how the design of such a regime shapes the trade-off between…

This paper presents a multi-period mixed-integer linear programming (MILP) framework for planning the transition from conventional to electric aircraft in regional aviation. The model jointly optimizes fleet acquisition, infrastructure…

This paper develops a three-currency Heath-Jarrow-Morton framework in which corporate credit is treated as a separate economy, connected to the nominal and real economies through synthetic inflation and credit exchange rates. The framework…

We introduce a simplicial and categorical formulation of Aharonov-Bohm (AB) type arbitrage in filtered market systems. Given a filtration modeled as a contravariant functor $F : \mathcal T^{op} \to \mathbf{Prob},$ we consider the associated…

This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…