This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of...This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.展开更多
In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposa...In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.展开更多
The transformation of characteristic functions is an effective way to avoid time-inconsistency of cooperative solutions in dynamic games.There are several forms on the transformation of characteristic functions.In thi...The transformation of characteristic functions is an effective way to avoid time-inconsistency of cooperative solutions in dynamic games.There are several forms on the transformation of characteristic functions.In this paper,a class of general transformation of characteristic functions is proposed.It can lead to the time-consistency of cooperative solutions and guarantee that the irrational-behaviorproof conditions hold true.To illustrate the theory,an example of dynamic game on a tree is given.展开更多
基金the National Natural Science Foundation of China under Grant Nos.11201335,11301376,and 71573110
文摘This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.
基金Supported in part by the Natural Science Foundation of Hubei Province under Grant 2015CKB737the National Natural Science Foundation of China under Grant No.11371284
文摘In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.
基金the National Natural Science Foundation of China under Grant No.71571108China Postdoctoral Science Foundation Funded Project under Grant No.2016M600525Qingdao Postdoctoral Application Research Project under Grant No.2016029。
文摘The transformation of characteristic functions is an effective way to avoid time-inconsistency of cooperative solutions in dynamic games.There are several forms on the transformation of characteristic functions.In this paper,a class of general transformation of characteristic functions is proposed.It can lead to the time-consistency of cooperative solutions and guarantee that the irrational-behaviorproof conditions hold true.To illustrate the theory,an example of dynamic game on a tree is given.
