2023/11/11 by Ying Hu, Hu, Ying, Xiaomin Shi +3
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Monetary Policy and Economic Impact #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2311.06512
In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for one-dimensional case. Using these and other delicate tools, we then construct solutions to coupled two-dimensional stochastic Riccati equation with jumps in both standard and singular cases. In the end, these results are applied to solve a cone-constrained stochastic linear-quadratic and a mean-variance portfolio selection problem with jumps. Different from no jump problems, the optimal (relative) state processes may change their signs, which is of course due to the presence of jumps.