One kind of linear-quadratic zero-sum stochastic differential game with jumps

Abstract

This paper is concerned with one kind of two-person zero-sum linear-quadratic stochastic differential game with jumps. A closed-loop formulation for the saddle points of the game is established in a mixed-strategy-law form, for which the associated Riccati equation and Hamiltonian system are solved.

Keywords:

• Stochastic linear-quadratic problem
• differential game
• saddle point
• Riccati equation

AMS subject classifications:

• 60H10
• 49N10
• 49N70
• 93E20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [11871310], the National Key R&D Program of China [2018YFA0703900], the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions [1716009], the Special Funds of Taishan Scholar Project [tsqn20161041], and the Colleges and Universities Youth Innovation Technology Program of Shandong Province [2019KJI011].