Constrained zero-sum LQ differential games for jump-diffusion systems with random coefficients
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918446759936000 |
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| author | Tang, Yanyan Li, Xun Xiong, Jie |
| author_facet | Tang, Yanyan Li, Xun Xiong, Jie |
| contents | This paper investigates a cone-constrained two-player zero-sum stochastic linear-quadratic (SLQ) differential game for stochastic differential equations (SDEs) with regime switching and random coefficients driven by a jump-diffusion process. Under the uniform convexity-concavity (UCC) condition, we establish the open-loop solvability of the game and characterize the open-loop saddle point via the forward-backward stochastic differential equations (FBSDEs). However, since both controls are constrained, the classical four-step scheme fails to provide an explicit expression for the saddle point. To overcome this, by employing Meyer's Itô formula together with the method of completing the square, we derive a closed-loop representation for the open-loop saddle point based on solutions to a new kind of multidimensional indefinite extended stochastic Riccati equations with jumps (IESREJs). Furthermore, for a special case, we prove the existence of solutions to IESREJs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constrained zero-sum LQ differential games for jump-diffusion systems with random coefficients Tang, Yanyan Li, Xun Xiong, Jie Optimization and Control Probability This paper investigates a cone-constrained two-player zero-sum stochastic linear-quadratic (SLQ) differential game for stochastic differential equations (SDEs) with regime switching and random coefficients driven by a jump-diffusion process. Under the uniform convexity-concavity (UCC) condition, we establish the open-loop solvability of the game and characterize the open-loop saddle point via the forward-backward stochastic differential equations (FBSDEs). However, since both controls are constrained, the classical four-step scheme fails to provide an explicit expression for the saddle point. To overcome this, by employing Meyer's Itô formula together with the method of completing the square, we derive a closed-loop representation for the open-loop saddle point based on solutions to a new kind of multidimensional indefinite extended stochastic Riccati equations with jumps (IESREJs). Furthermore, for a special case, we prove the existence of solutions to IESREJs. |
| title | Constrained zero-sum LQ differential games for jump-diffusion systems with random coefficients |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2603.07428 |