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Open-loop and closed-loop solvabilities for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
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Open-loop and closed-loop solvabilities for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
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This paper investigates zero-sum stochastic linear quadratic (SLQ) differential games with Markovian jumps. Open-loop and closed-loop solvabilities are studied by employing a new ``decomposition method", which decomposes the open-loop and closed-loop solvability problems of zero-sum SLQ differential games into two coupled SLQ control problems. Under the uniform convexity-concavity condition, we construct the open-loop saddle point along with its closed-loop representation based on the solution to a system of constrained coupled differential Riccati equations (CDREs), whose solvability is also established by employing the dimension extension technique and the continuation method. Finally, we provide a concrete example and present its closed-form saddle point based on the theoretical results obtained.
Forward citations
Cited by 3 Pith papers
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Constrained Zero-Sum Stochastic Linear-Quadratic Differential Game for Jump-Diffusion Systems with Random Coefficients
Under the uniform convexity-concavity condition, the authors derive a closed-loop representation of the open-loop saddle point for constrained zero-sum SLQ games via solutions to indefinite extended stochastic Riccati...
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Constrained Zero-Sum Stochastic Linear-Quadratic Differential Game for Jump-Diffusion Systems with Random Coefficients
For a zero-sum stochastic linear-quadratic differential game with jumps, random coefficients and cone constraints, the paper proves a unique saddle point under convexity-concavity and derives a feedback form, with exi...
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Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
Finite-horizon optimal feedback gains in zero-sum stochastic linear-quadratic games with regime switching converge exponentially to infinite-horizon gains, yielding a turnpike theorem for the optimal triple.
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