Indefinite stochastic linear-quadratic optimal control problems with random jumps and related stochastic Riccati equations
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We discuss the stochastic linear-quadratic (LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes (SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.
Keywordsstochastic linear-quadratic problem Hamiltonian system Riccati equation Poisson process indefinite case
MSC(2010)93E20 60H10 49N10
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This work was supported by National Natural Science Foundation of China (Grant Nos. 61573217, 11471192 and 11626142), the National High-Level Personnel of Special Support Program, the Chang Jiang Scholar Program of Chinese Education Ministry, the Natural Science Foundation of Shandong Province (Grant Nos. JQ201401 and ZR2016AB08), the Colleges and Universities Science and Technology Plan Project of Shandong Province (Grant No. J16LI55) and the Fostering Project of Dominant Discipline and Talent Team of Shandong University of Finance and Economics.
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