Research On Models Of Pension Funds By Stochastic Control Approach

One of the important means to keep the value and increment of the pension fund is to invest the pension fund to the financial market, and there is increasing pension fund that is being or has been invested to the financial market in more and more countries. The pension fund has the feature of both sociality and finance. As for as the trait of finance, its investment benefit is greatly influenced by the strategy of asset allocation; and on the trait of sociality, there are some special factors to be calculated in the investment process such as constraint of no short-selling and no lowering, a certain guaranteed safety level (or it is called solvency level) of the final fund asked by the supervisory authority or law, etc.During the social and economical development, the defined contribution (DC) pension fund is to be paid more and more attention in all of the countries; and it covers more and more proportions in the pension guarantee system in those coun-tries. In the point of view of the fund manager, the asset allocation of the DC pension fund can be divided into two parts of accumulation phase and stationary regime and can be studied separately; in the point of view of the pensioner, the asset allocation of the DC pension fund can be divided into both accumulation phase and decumulation phase and can be discussed separately.In this thesis, firstly, we propose a continuous-time stochastic control model of optimal allocation for a DC pension fund with a minimum guarantee. Under the framework of an optimal stochastic control problem with state constraints and the dividend payment of the stock, we adopt the view of a pension fund manager maximizing the expected power utility from the fund wealth on an infinite horizon. The explicit expressions for both the optimal allocation strategy in feedback form and the value function which is a solution to the HJB equation are obtained by the stochastic control method.Secondly, under Knightian uncertainty, we propose a continuous-time stochas-tic control model of optimal management for a DC pension fund with a minimum guarantee. We characterize a pension fund manager’s utility from the fund wealth on an infinite horizon by a-maxmin expected utility (a-MEU). in which he differ- entiates ambiguity and ambiguity attitude. Pension fund manager’s value function is derived by the stochastic control theory. The explicit expressions for both the optimal allocation strategy in feedback form and the value function are obtained.Thirdly, in the decumulation phase of DC pension fund, the retiree choose in-come drawdown option to reduce annuity risk. A optimal portfolio choice model for pension fund with inflation is given. The expectedly quadratic loss function mini-mum could be used to represent the pensioner’s investment goals. We obtain some properties of the value function. Through the variable transformation, we present the dynamic programming principle and obtain that value function is the viscosity solution of HJB equation satisfying the boundary value problem. Meanwhile, the investment of pension fund is required no short-selling and is constrained that the final fund cannot be lower than a certain guaranteed safety level.Finally, in the whole paper, financial market is complete in which risky asset prices follow a geometric Brownian motion. Some mathematical methods are mainly utilized to study, such as optimal stochastic control, infinite time interval backward stochastic differential equations (BSDEs), dynamic programming approach, etc.