Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914756855595008 |
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| author | Gomoyunov, Mikhail I. |
| author_facet | Gomoyunov, Mikhail I. |
| contents | We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and second players are, respectively, to minimize and maximize a given cost functional. We propose a way of how the dynamic programming principle can be formalized and the theory of generalized (viscosity) solutions of path-dependent Hamilton--Jacobi equations can be developed in order to prove the existence of the game value, obtain a characterization of the value functional, and construct players' optimal feedback strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations Gomoyunov, Mikhail I. Optimization and Control Dynamical Systems 45D05, 49L20, 49L25, 49N70 We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and second players are, respectively, to minimize and maximize a given cost functional. We propose a way of how the dynamic programming principle can be formalized and the theory of generalized (viscosity) solutions of path-dependent Hamilton--Jacobi equations can be developed in order to prove the existence of the game value, obtain a characterization of the value functional, and construct players' optimal feedback strategies. |
| title | Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations |
| topic | Optimization and Control Dynamical Systems 45D05, 49L20, 49L25, 49N70 |
| url | https://arxiv.org/abs/2404.10428 |