arXiv subjects

Weilun Cheng

Publications and source records attributed to Weilun Cheng.

3 recordsLinked to original sources

arXiv2026

Mean-field game of mean-variance portfolio optimization with peer-based risk aversion

This paper investigates a class of mean-field game (MFG) for mean-variance (MV) portfolio optimization, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a piecewise form that depends on whether the individual's wealth is above or below the population average, leading to a time-inconsistent MFG. Our goal is to seek a mean-field equilibrium, characterized by a forward-backward stochastic differential equation (FBSDE) system and a mean-field consistency condition. The new challenge stems from the discontinuous coefficients induced by the piecewise risk aversion. In response, we first introduce a smooth regularization technique to establish the existence of a solution to the discontinuous multidimensional FBSDE; this solution then yields the existence of an intra-personal equilibrium for the representative agent. Finally, we conclude the existence of the mean-field equilibrium in the time-inconsistent MFG by invoking fixed-point arguments and convergence analysis as the smoothing regularization vanishes.

q-fin.MF↗

arXiv2025

Equilibrium Investment with Random Risk Aversion: (Non-)uniqueness, Optimality, and Comparative Statics

This paper studies a continuous-time portfolio selection problem under a general distribution of random risk aversion (RRA). We provide a complete characterization of all deterministic equilibrium strategies in closed form. Our results show that the structure of the solution depends crucially on the distribution of RRA: the equilibrium is unique (if exits) when the expectation of RRA is finite, whereas an infinite expectation leads either to infinitely many equilibria or to a unique trivial one (i.e. risk-free investment). To resolve this multiplicity of equilibria, we select, among all deterministic equilibria, the one that maximizes the objective functional at the initial time. We establish a necessary and sufficient condition for the existence of such an optimal equilibrium, which is then shown to be unique and uniformly optimal. Finally, we conduct a comparative statics. Using counterexamples based on two-point distributed RRA, we demonstrate that a larger risk aversion in the sense of first-order stochastic dominance does not necessarily lead to less risky investment. Within the two-point distribution framework, we further examine the single-crossing property of equilibrium strategies and the monotonicity of the crossing time. We show that a larger risk aversion under a stronger stochastic order -- the reverse hazard rate order -- always leads to less risky investment. In addition, we analyze how the convex combination of independent and identically distributed RRAs influences investment.

q-fin.MF↗

arXiv2025

MF-VITON: High-Fidelity Mask-Free Virtual Try-On with Minimal Input

Recent advancements in Virtual Try-On (VITON) have significantly improved image realism and garment detail preservation, driven by powerful text-to-image (T2I) diffusion models. However, existing methods often rely on user-provided masks, introducing complexity and performance degradation due to imperfect inputs, as shown in Fig.1(a). To address this, we propose a Mask-Free VITON (MF-VITON) framework that achieves realistic VITON using only a single person image and a target garment, eliminating the requirement for auxiliary masks. Our approach introduces a novel two-stage pipeline: (1) We leverage existing Mask-based VITON models to synthesize a high-quality dataset. This dataset contains diverse, realistic pairs of person images and corresponding garments, augmented with varied backgrounds to mimic real-world scenarios. (2) The pre-trained Mask-based model is fine-tuned on the generated dataset, enabling garment transfer without mask dependencies. This stage simplifies the input requirements while preserving garment texture and shape fidelity. Our framework achieves state-of-the-art (SOTA) performance regarding garment transfer accuracy and visual realism. Notably, the proposed Mask-Free model significantly outperforms existing Mask-based approaches, setting a new benchmark and demonstrating a substantial lead over previous approaches. For more details, visit our project page: https://zhenchenwan.github.io/MF-VITON/.

cs.CV↗