Abstract:This paper studies a two-player zero-sum stochastic linear-quadratic (SLQ) differential game for controlled jump-diffusion systems with random coefficients, where the controls of both players are constrained to nonempty closed convex cones. Under a uniform convexity--concavity condition, we establish the existence and uniqueness of an open-loop saddle point and characterize it by a forward--backward stochastic differential equation with jumps (FBSDEJ) together with cone-type variational inequalities. Assuming the existence of positive bounded solutions to the associated system of indefinite extended stochastic Riccati equations with jumps (IESREJs), we derive a feedback-form representation of the unique open-loop saddle point by constructing predictable minimax selectors and combining the Meyer--Itô formula with jumps, and the FBSDEJ characterization. Finally, under additional structural conditions, we prove the existence of positive bounded solutions to the IESREJs by a double-truncation approximation and a multidimensional BSDEJ comparison theorem.
From: Yanyan Tang [view email]
[v1]
Sun, 8 Mar 2026 02:50:27 UTC (25 KB)
[v2]
Mon, 30 Mar 2026 07:46:10 UTC (23 KB)
[v3]
Fri, 3 Apr 2026 02:14:08 UTC (23 KB)
[v4]
Wed, 15 Apr 2026 06:49:39 UTC (23 KB)
[v5]
Fri, 24 Jul 2026 01:56:28 UTC (31 KB)
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