Abstract. The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed linear-quadratic optimal control problem for a fully coupled forward-backward doubly stochastic system. Mathematics Subject Classification. 93E20, 60H10.
To get rid of the development dilemma of green credit, we constructed a stochastic evolutionary game model of local government, commercial banks, and loan enterprises. We gave sufficient conditions for the stability of strategy based on the stability discriminant theorem of
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stochastic differential equation (SDE). Then, we discussed the impacts of incentive and penalty parameters on green credit. Through the above analysis, we got the following conclusions: (1) rewards and punishments always benefit green production and green credit, but increasing incentives is not conducive to the governments’ performance of regulatory duties; (2) punishments can better improve the convergence rate of players’ strategy than rewards; and (3) both rewards and punishments can exert an obvious effect in improving the changing degree of players’ strategy. Finally, we put forward some suggestions to optimize the green credit mechanism.
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