2011/11/20 by Qian Lin, Lin, Qian
Economics, Econometrics and Finance · Social Sciences · Decision Sciences · #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1111.4642
In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian motion and Poisson random measure. For this end, we first study the regularity of solutions for this kind of forward-backward stochastic differential equations. We obtain that the value function is a deterministic function and satisfies the dynamic programming principle for this kind of optimal control problem. Moreover, we prove that the value functions is a viscosity solutions of the associated Hamilton-Jacobi-Bellman equations with integral-differential operators.