arXiv subjects

Jingtao Lin

Publications and source records attributed to Jingtao Lin.

3 recordsLinked to original sources

arXiv2026

A Partially Observed Stochastic Linear Stackelberg Differential Game with Poisson Jumps under Mean-Variance Criteria

In this paper, a partially observed stochastic linear Stackelberg differential game with mean-variance criteria is studied. Randomness comes from Brownian motions and Poisson random measures. which leads to a circular dependency. We follow the orthogonal decomposition method to overcome the circular dependency of the control and state processes. Both original problems of the follower and leader are decomposed into several fully observed problems with mean-variance criteria. During these processes, non-linear stochastic filtering with Poisson random measures, developed in this paper, plays an important role. Besides the follower's problem is embedded into a class of auxiliary stochastic linear-quadratic optimal control problem of stochastic differential equations with Poisson jumps, the leader's problem is also embedded into a class of auxiliary stochastic linear-quadratic optimal control problem of forward-backward stochastic differential equations with Poisson jumps. Observable state feedback Stackelberg equilibria are obtained, via some Riccati equations.

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arXiv2025

Global Maximum Principle for Partially Observed Risk-Sensitive Progressive Optimal Control of FBSDE with Poisson Jumps

This paper is concerned with one kind of partially observed progressive optimal control problems of coupled forward-backward stochastic systems driven by both Brownian motion and Poisson random measure with risk-sensitive criteria. The control domain is not necessarily convex, and the control variable can enters into all the coefficients. The observation equation also has correlated noises with the state equation. Under the Poisson jump setting, the original problem is equivalent to a complete information stochastic recursive optimal control problem of a forward-backward system with quadratic-exponential generator. In order to establish the first- and second-order variations, some new techniques are introduced to overcome difficulties caused by the quadratic-exponential feature. A new global stochastic maximum principle is deduced. As an application, a risk-sensitive optimal investment problem with factor model is studied. Moreover, the risk-sensitive stochastic filtering problem is also studied, which involves both Brownian and Poissonian correlated noises. A modified Zakai equation is obtained.

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arXiv2023

A Risk-Sensitive Global Maximum Principle for Controlled Fully Coupled FBSDEs with Applications

This paper is concerned with a kind of risk-sensitive optimal control problem for fully coupled forward-backward stochastic systems. The control variable enters the diffusion term of the state equation and the control domain is not necessarily convex. A new global maximum principle is obtained without assuming that the value function is smooth. The maximum condition, the first- and second-order adjoint equations heavily depend on the risk-sensitive parameter. An optimal control problem with a fully coupled linear forward-backward stochastic system and an exponential-quadratic cost functional is discussed. The optimal feedback control and optimal cost are obtained by using Girsanov's theorem and completion-of-squares approach via risk-sensitive Riccati equations. A local solvability result of coupled risk-sensitive Riccati equations is given by Picard-Lindel$\ddot{o}$f's Theorem.

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