Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein–Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility.     

一类终端财富期望效用最大化问题: 通货膨胀情形

本文研究了一类受通货膨胀影响的终端财富期望效用最大化问题.对常数相对风险厌恶(CRRA) 情形的效用函数,用直接构造的方法得到了代理人的显式最优投资策略和最大期望效用,并给出其经济含义. 该思想来自线性二次最优控制问题中的完全平方技术.根据股票价格和通货膨胀率的历史数据,我们用SAS软件估计出模型中参数的近似值,并给出代理人的最优投资策略和最大期望效用.     

Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework

This paper investigates an optimal investment strategy of DC pension plan in a stochastic interest rate and stochastic volatility framework. We apply an affine model including the Cox–Ingersoll–Ross (CIR) model and the Vasicek mode to characterize the interest rate while the stock price is given by the Heston’s stochastic volatility (SV) model. The pension manager can invest in cash, bond and stock in the financial market. Thus, the wealth of the pension fund is influenced by the financial risks in the market and the stochastic contribution from the fund participant. The goal of the fund manager is, coping with the contribution rate, to maximize the expectation of the constant relative risk aversion (CRRA) utility of the terminal value of the pension fund over a guarantee which serves as an annuity after retirement. We first transform the problem into a single investment problem, then derive an explicit solution via the stochastic programming method. Finally, the numerical analysis is given to show the impact of financial parameters on the optimal strategies.     

通胀环境下股价波动率具有奈特不确定的最优消费与投资问题

本文在通胀环境和连续时间模型假设下,研究股票价格波动率具有奈特不确定对投资者的最优消费和投资策略的影响．首先在通胀环境和股票价格波动率具有奈特不确定的条件下,建立最优消费与投资问题的随机控制数学模型,得到了最优消费与投资所满足的HJB方程,并在常相对风险厌恶效用的情形下,获得最优化问题值函数的显式解．其次在通胀环境中当股价波动率具有奈特不确定时,得到了含糊厌恶的投资者是基于股价波动率的上界作出决策,并给出了投资者的最优投资和消费策略．最后在给定参数的条件下,对所得结果进行数值模拟和经济分析．     

常数比例投资组合保险(CPPI)策略 --捐赠型基金投资策略的最优选择

本文采用Merton提出的处理捐赠型基金的连续时间模型的一般框架，分析了在风险资产为几何布朗运动，效用函数为CRRA效用函数，且捐赠型基金有动态最低支出时的最优支出策略和最优投资策略，结果表明存在一条策略基准线，当基金的总资产在策略基准线之上时，基金管理人关于基金支出与投资策略的选择与不存在最低支出的要求时所作出的决策是一样的，但是一旦基金的总资产低于这条策略基准线时，基金管理人便需要考虑到基金将来必要的支出，并实际影响到他对投资策略的选择，此时基金管理人可作的最优选择是：最低的支出和一种为复制幂收益函数期权的CPPI投资策略。     

Comparison of optimal portfolios with and without subsistence consumption constraints

We present the effects of the subsistence consumption constraints on a portfolio selection problem for an agent who is free to choose when to retire with a constant relative risk aversion (CRRA) utility function. By comparing the previous studies with and without the constraints expressed by the minimum consumption requirement, the changes of a retirement wealth level and the amount of money invested in the risky asset are derived explicitly. As a result, the subsistence constraints always lead to lower retirement wealth level but do not always induce less investment in the risky asset. This implies that even though the agent who has a restriction on consumption retires with lower wealth level, she invests more money near the retirement when her risk aversion lies inside a certain range.     

基于混合跳扩散模型的最优投资消费和寿险购买策略研究

本文研究在混合跳扩散模型下投资者分别投资于寿险、零息债券和股票时,关于最优投资消费和寿险购买的随机策略问题。通过构造满足混合跳扩散模型的金融市场、保险市场和可容许策略,在CRRA(constant relative risk aversion)效用下,利用动态规划的方法求解了对应的HJB方程,获得了值函数和最优策略的显式表达式。为了探索模型的有效性,本文给出了相对风险厌恶系数的数值分析以及相关参数对最优策略的影响。     

跳扩散最优控制的随机最大值原理及在金融中的应用

讨论了由金融市场中投资组合和消费选择问题引出的一类最优控制问题,投资者的期望效用是常数相对风险厌恶(CRRA)情形.在跳扩散框架下,利用古典变分法得到了一个局部随机最大值原理.结果应用到最优投资组合和消费选择策略问题,得到了状态反馈形式的显式最优解.     

Horizon-unbiased utility functions

In this paper we consider a class of mixed optimal control/optimal stopping problems related to the choice of the best time to sell a single unit of an indivisible asset. We assume that in addition to the indivisible asset, the agent has access to a financial market. Investments in the financial market can be used for hedging, but the financial assets are only partially correlated with the indivisible asset, so that the agent faces an incomplete markets problem.