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Indexed by:期刊论文

Date of Publication:2018-11-01

Journal:JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Included Journals:SCIE、SSCI

Volume:179

Issue:2,SI

Page Number:501-532

ISSN No.:0022-3239

Key Words:Necessary optimality conditions; Sufficient optimality conditions; Regular-singular control; Stochastic differential game; Asymmetric information; Saddle point; Nash equilibrium; Optimal investment; Dividend; Model uncertainty; 91G80; 91A15; 91A23; 93E20; 60J75; 91B28; 91B30

Abstract:We consider a class of regular-singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular-singular game with asymmetric information, and then the Nash equilibrium point is characterized.