The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic...The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.展开更多
This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple ris...This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic （LQ） control theory with no-shorting constraint. Then the efficient strategy （optimal investment strategy） and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman （HJB） equation.展开更多
基金The article was prepared within the framework of the HSE University Basic Research Program in 2023。
文摘The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10871102 and Speaialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20090031110001.
文摘This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic （LQ） control theory with no-shorting constraint. Then the efficient strategy （optimal investment strategy） and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman （HJB） equation.
