In this paper,we study the infinite-time mean field games with discounting,establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution.To solve this problem,we p...In this paper,we study the infinite-time mean field games with discounting,establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution.To solve this problem,we partition all agents into a representative player and the social equilibrium.When the optimal strategy of the representative player has the same feedback form as the strategy in the social equilibrium,we say that the system achieves a Nash equilibrium.We construct a Nash equilibrium using the stochastic maximum principle and infinite-time forward-backward stochastic differential equations(FBSDEs).By employing elliptic master equations,a class of distribution-dependent elliptic partial differential equations(PDEs),we provide a representation for the Nash equilibrium strategies.We prove the Yamada−Watanabe type theorem and show weak uniqueness for infinite-time FBSDEs.Furthermore,we prove that the solutions to a system of infinite-time FBSDEs can be employed to construct viscosity solutions for a class of distribution-dependent elliptic PDEs.展开更多
In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to deri...In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.展开更多
In this paper, infinite-time p-admissibility of unbounded operators is introduced and the C0-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the a...In this paper, infinite-time p-admissibility of unbounded operators is introduced and the C0-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.展开更多
基金supported by National Key R&D Program of China(Grant Nos.2024YFA1013503 and 2020YFA0712700)the National Natural Science Foundation of China(Grant No.12431017)。
文摘In this paper,we study the infinite-time mean field games with discounting,establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution.To solve this problem,we partition all agents into a representative player and the social equilibrium.When the optimal strategy of the representative player has the same feedback form as the strategy in the social equilibrium,we say that the system achieves a Nash equilibrium.We construct a Nash equilibrium using the stochastic maximum principle and infinite-time forward-backward stochastic differential equations(FBSDEs).By employing elliptic master equations,a class of distribution-dependent elliptic partial differential equations(PDEs),we provide a representation for the Nash equilibrium strategies.We prove the Yamada−Watanabe type theorem and show weak uniqueness for infinite-time FBSDEs.Furthermore,we prove that the solutions to a system of infinite-time FBSDEs can be employed to construct viscosity solutions for a class of distribution-dependent elliptic PDEs.
基金Supported by the Natural Science Foundation of China(No.71071071,11101205)Ministry of Education Social Science Research Fund Planning Project,China Postdoctoral Science Foundation(No.200902507,20080431079)+1 种基金Nanjing University of Finance&Economics Science Research Foundation(2012Y1204)the Natural Sciences and Engineering Research Council of Canada(NSERC)
文摘In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.
文摘In this paper, infinite-time p-admissibility of unbounded operators is introduced and the C0-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.
