arXiv subjects

Guojiang Shao

Publications and source records attributed to Guojiang Shao.

5 recordsLinked to original sources

arXiv2026

A Computable Stochastic Riccati Equations Framework for Mean--Variance Portfolio Selection with Multifactor Stochastic Volatility Model

We investigate a computable and empirically implementable framework for continuous-time mean--variance optimal portfolio selection with random market coefficients. The market model is built on a tractable multifactor stochastic volatility structure, which captures state-dependent risk premia, stochastic volatility, and dynamic cross-asset dependence. The optimal control is characterized by stochastic Riccati equations. On the computational side, we design an iterative BSDE-based procedure to approximate the stochastic Riccati equation from above and below, where the initial upper and lower bounds are obtained by solving two linear BSDEs. We then apply a logarithmic transformation to remove the singularity in the SRE, and solve the resulting transformed equation using both Deep BSDE and DBDP methods. The linear BSDE bounds also provide effective initial-value estimates, improving the convergence speed and training stability of the Deep BSDE solver. Empirical experiments based on sector ETF data show that the proposed multifactor mean--variance strategy produces smooth target-return wealth dynamics, with improved drawdown control and downside-risk protection relative to benchmark strategies. These results demonstrate the practical potential of combining stochastic Riccati equations, neural BSDE solvers, and multifactor market modeling for dynamic asset allocation.

math.OC↗

arXiv2026

Stochastic LQ Optimal Control with Random Coefficients and a Terminal Mean-Field Cost

This paper investigates a multidimensional non-homogeneous stochastic linear-quadratic optimal control problem featuring random coefficients and a terminal mean-field term in the cost functional, enabling its direct application to mean-variance models in financial engineering. Employing the Lagrangian duality method together with a decomposition approach for linear backward stochastic differential equations, we provide two types of sufficient conditions for solvability and derive the corresponding optimal controls. In particular, in the deterministic-coefficient case, our condition is weaker than the standard condition found in the existing literature on mean-field stochastic LQ problems. Finally, a numerical example drawn from optimal portfolio selection with multiple assets under mean-variance utility demonstrates the applicability of our results.

math.OC↗

arXiv2025

Competitive optimal portfolio selection under mean-variance criterion

We investigate a portfolio selection problem involving multi competitive agents, each exhibiting mean-variance preferences. Unlike classical models, each agent's utility is determined by their relative wealth compared to the average wealth of all agents, introducing a competitive dynamic into the optimization framework. To address this game-theoretic problem, we first reformulate the mean-variance criterion as a constrained, non-homogeneous stochastic linear-quadratic control problem and derive the corresponding optimal feedback strategies. The existence of Nash equilibria is shown to depend on the well-posedness of a complex, coupled system of equations. Employing decoupling techniques, we reduce the well-posedness analysis to the solvability of a novel class of multi-dimensional linear backward stochastic differential equations (BSDEs). We solve a new type of nonlinear BSDEs (including the above linear one as a special case) using fixed-point theory. Depending on the interplay between market and competition parameters, three distinct scenarios arise: (i) the existence of a unique Nash equilibrium, (ii) the absence of any Nash equilibrium, and (iii) the existence of infinitely many Nash equilibria. These scenarios are rigorously characterized and discussed in detail.

math.OC↗

arXiv2025

Sharp Estimates for Optimal Multistage Group Partition Testing

In multistage group testing, the tests within the same stage are considered nonadaptive, while those conducted across different stages are adaptive. Specifically, when the pools within the same stage are disjoint, meaning that the entire set is divided into several disjoint subgroups, it is referred to as a multistage group partition testing problem, denoted as the (n, d, s) problem, where n, d, and s represent the total number of items, defectives, and stages respectively. This paper presents exact solutions for the (n, 1, s) and (n, d, 2) problems for the first time. Additionally, a general dynamic programming approach is developed for the (n, d, s) problem. Significantly we give the sharp upper and lower bounds estimates. If the defective number in unknown but bounded, we can provide an algorithm with an optimal competitive ratio in the asymptotic sense. While assuming the prior distribution of the defective items, we also establish a well performing upper and lower bound estimate to the expectation of optimal strategy

cs.IT↗

arXiv2025

AB-Cache: Training-Free Acceleration of Diffusion Models via Adams-Bashforth Cached Feature Reuse

Diffusion models have demonstrated remarkable success in generative tasks, yet their iterative denoising process results in slow inference, limiting their practicality. While existing acceleration methods exploit the well-known U-shaped similarity pattern between adjacent steps through caching mechanisms, they lack theoretical foundation and rely on simplistic computation reuse, often leading to performance degradation. In this work, we provide a theoretical understanding by analyzing the denoising process through the second-order Adams-Bashforth method, revealing a linear relationship between the outputs of consecutive steps. This analysis explains why the outputs of adjacent steps exhibit a U-shaped pattern. Furthermore, extending Adams-Bashforth method to higher order, we propose a novel caching-based acceleration approach for diffusion models, instead of directly reusing cached results, with a truncation error bound of only $O(h^k)$ where $h$ is the step size. Extensive validation across diverse image and video diffusion models (including HunyuanVideo and FLUX.1-dev) with various schedulers demonstrates our method's effectiveness in achieving nearly $3\times$ speedup while maintaining original performance levels, offering a practical real-time solution without compromising generation quality.

stat.ML↗