2025/04/07 by Jingtao Lin, Lin, Jingtao, Jingtao Shi +1
Decision Sciences · Economics, Econometrics and Finance · Engineering · #49K45 #49N70 #60H10 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stability and Control of Uncertain Systems #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2504.04649
openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.