This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from th...This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer： The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer＇s optimal investment strategies under the two cases.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
This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic ris...This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic risk process is perturbed by a standard Brownian motion.The insurer can invest in multiple risky assets and one risk-free asset and the correlations between the risky assets and the risk process are considered.Optimal strategy is obtained explicitly,which is a function of time and related to the risk process.The effects of market parameters on the optimal strategy are discussed and a numerical example is also given.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11201335 and 11301376
文摘This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer： The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer＇s optimal investment strategies under the two cases.
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.
基金supported by the Natural Science Foundation of Tianjin under Grant No.09JCYBJC01800
文摘This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic risk process is perturbed by a standard Brownian motion.The insurer can invest in multiple risky assets and one risk-free asset and the correlations between the risky assets and the risk process are considered.Optimal strategy is obtained explicitly,which is a function of time and related to the risk process.The effects of market parameters on the optimal strategy are discussed and a numerical example is also given.
