martingale measure analysis

In jump-diffusion incomplete markets, derivative pricing and hedging lack a unique arbitrage-free solution due to multiple sources of incompleteness—including jumps, asymmetric information, and volatility uncertainty. Method: This paper proposes a novel approach integrating filtration reduction and consistency enhancement: first constructing a fictitious complete market via filtration reduction, then recovering a unique equivalent martingale measure (EMM) in the original incomplete space through consistency constraints. Contribution/Results: This is the first systematic unification of these two techniques to jointly address multifaceted incompleteness. Under frictionless, competitive market assumptions, the method rigorously yields a unique arbitrage-free price and a dynamic hedging strategy for derivatives. It supports progressive generalization—from simple to fully specified models—and establishes an operational, unified pricing paradigm for jump-diffusion frameworks.

This paper investigates distributionally robust sensitivity analysis of model risk under martingale constraints—or equivalently, fixed first-order marginal distributions—in the Wasserstein space. We propose the first unified framework jointly modeling distributionally robust minimization and semi-static hedging, yielding explicit closed-form solutions for first-order optimal hedging strategies. Our methodology integrates Wasserstein probability metrics, martingale-constrained optimization, and semi-static derivative hedging theory, providing a unified characterization of robustness bounds under both standard and generalized Wasserstein distances. The main contributions are: (1) a novel paradigm for quantifying first-order sensitivity of model risk; (2) implementable, analytically tractable optimal semi-static hedging strategies; and (3) an extension of distributionally robust financial modeling to non-i.i.d., non-Markov, path-dependent settings—substantially enhancing robustness and practical applicability in real-world markets.

This paper addresses the problem of constructing a measure-preserving martingale interpolation between prescribed marginal distributions in arbitrary dimensions, such that the resulting process is as close as possible to Brownian motion. Departing from prior work—largely restricted to one dimension and requiring finite second moments—we propose the first algorithm applicable under the significantly weaker assumption that marginals possess finite moments of order strictly greater than one. Our method establishes a novel connection between Bass martingales and semimartingale optimal transport, leading to the Measure-Preserving Martingale Sinkhorn (MPMS) algorithm. MPMS is derived from a dual formulation and integrates stochastic analysis, optimal transport, and fixed-point theory. We rigorously prove its monotonic convergence and dimensional scalability. Empirical evaluations on both synthetic and real financial datasets demonstrate that MPMS consistently outperforms existing approaches in accuracy and stability.

This paper identifies an error in a corollary of Theorem 2.8 in Bayraktar & Yu (2018), undermining their market viability conclusion under proportional transaction costs. To address feasibility, it proposes strict consistent local martingale systems (SCLMS) — replacing the conventional strict consistent pricing systems — as the dual criterion, and constructs a unified verification framework based on two weak no-arbitrage conditions: NUPBR (no unbounded profit with bounded risk) and the newly introduced NLABP (no local acceptable profit). It establishes, for the first time, the robust equivalence between SCLMS and both NUPBR and NLABP. The introduction of NLABP extends the scope of arbitrage-free theory to broader settings with transaction costs. Finally, the paper derives necessary and sufficient conditions for market viability under proportional transaction costs, providing a novel theoretical foundation for utility maximization in frictional markets.

This paper addresses the challenge of modeling dynamic risk measures for continuous-time stochastic processes with time-varying returns. Method: It introduces a novel framework based on geometric backward stochastic differential equations (GBSDEs) and doubly driven BSDEs. The authors first systematically develop the theoretical foundation of GBSDEs; then establish existence, regularity, uniqueness, and stability of solutions to an auxiliary BSDE featuring a nonlinear driver of the form $y|ln y| + |z|^2/y$; finally, they systematically transfer these results to the doubly driven setting. Contribution: The work establishes a complete well-posedness theory for generalized BSDEs under both bounded and unbounded terminal conditions and coefficients. It provides the first precise characterization of the dynamic evolution of robust nonlinear risk measures—such as $L^p$-norm–based ones—thereby furnishing a unified geometric modeling foundation for star-shaped and return-based risk measures.

This study aims to unify the theoretical framework of probability measures in asset pricing by addressing how market prices can be represented through measure changes. It systematically traces the conceptual evolution from state prices and risk-neutral measures to stochastic discount factors (pricing kernels), emphasizing that asset pricing fundamentally relies on equivalent measures—adjusted via discounting, numéraire normalization, or utility weighting—rather than the original physical probability measure. The work innovatively incorporates data-driven information such as textual content, attention metrics, and sentiment into the measure transformation process, thereby extending the learning paradigm for pricing kernels in incomplete markets. By integrating stochastic discount factors, Radon–Nikodym derivatives, Girsanov transformations, implied densities, and machine learning techniques, the paper constructs a cohesive framework that bridges classical asset pricing theory with modern empirical methodologies, offering both theoretical grounding and practical guidance.

This work addresses the inconsistency between training and inference in existing speculative decoding methods, where training optimizes only a single greedy path while inference requires verifying multiple sampled paths. To bridge this gap, we introduce variational inference into speculative decoding for the first time, reformulating draft model training as posterior inference over latent proposal paths by maximizing the marginal probability of acceptance under the target model. We propose a path-level utility function, an EM-based optimization framework, and two novel mechanisms: Adaptive Rejection Weighting (ARW) and Confidence-Aware Regularization (CAR). Experiments demonstrate that our approach achieves up to 9.6% higher speedup than EAGLE-3 and a 7.9% improvement in acceptance rate over ViSpec across various large language and multimodal models, significantly enhancing inference efficiency.

This study addresses the absence of explicit solutions and verifiable conditions for local risk-minimizing (LRM) strategies in incomplete markets under exponential additive process models. Focusing on additive processes with time-dependent Lévy measures, the paper establishes, for the first time, a theoretical framework for LRM strategies by introducing integrability conditions on the Lévy measure, which enables the derivation of an explicit expression for the LRM strategy. The proposed approach is validated through a combination of stochastic analysis, additive process theory, and numerical simulations, using the variance gamma scaled self-decomposable process as a concrete example. By extending beyond the conventional limitations of Lévy processes, this work provides a practical and computationally tractable hedging tool for complex financial models.