CEV模型下时滞最优投资与再保险问题

在常方差弹性（constant elasticity of variance,CEV）模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

通胀风险与波动风险环境下带有保费返还条款的DC型养老金计划

通胀风险和波动风险是影响养老金计划的最重要的两个因素,保费返还条款可以保障死亡的养老基金持有者的权益.文章研究了通胀风险和波动风险环境下带有保费返还条款的确定缴费型(DC型)养老金计划问题.模型中假设风险资产价格由Heston随机波动率模型驱动,养老金被允许投资于一种无风险资产、一种风险资产和一种通胀相关指数债券.在均值-方差准则下,利用随机控制理论、博弈论和变量分离法得到了时间一致最优投资策略和有效前沿的显性解.最后通过应用数值算例对最优投资策略和有效前沿进行了敏感性分析.     

CEV模型下时滞最优投资与再保险问题

在常方差弹性(constant elasticity of variance,CEV)模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

考虑红利支付与提前退休的最优投资组合

研究了在经济代理人通过不可逆退休时间选择来调整劳动时间框架下的最优消费和投资问题,主要考虑风险资产派发红利的情形.运用随机控制方法,求解使得消费-闲暇预期效用最大化的最优策略.最优投资组合及最优退休时刻表明,代理人在为提前退休积累财富的同时,也能最佳享受消费和闲暇所带来的快乐.     

考虑模型不确定的TBP养老金的鲁棒最优投资策略研究

以目标收益养老金计划(TBP)模型研究鲁棒最优投资问题, 其中养老金管理者对模型参数不确定带来的风险是模糊风险厌恶的. 养老金管理者为规避风险和增加收益将投资于无风险资产和风险资产. 考虑连续时间情形, 假设养老金计划参保人的缴费是确定的, 而参保人的收益给付是确定目标收益给付, 资金账户的收益风险由不同代际的参保人共同承担, 同时考虑随机工资及其与金融市场的相关性. 以参保人退休后养老金给付偏离目标的风险和代际之间风险分担的组合最小化为投资决策目标, 并采用指数函数的形式描述实际给付与目标给付的偏离, 利用随机最优控制方法, 建立相应的HJB方程并求解得到最优投资收益策略和最优给付策略的解析解. 通过数值示例分析了模型参数对最优投资和最优给付策略的影响.     

基于动态VaR约束与随机波动率模型的最优投资策略

研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题. 假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产, 风险资产的价格过程由Stein-Stein随机波动率模型刻画. 同时, 投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法, 得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式; 并通过理论分析和数值算例, 阐述了动态VaR约束与随机波动率对最优投资策略的影响.     

通胀风险下基于HARA效用的DC型养老金计划

通货膨胀是养老基金管理过程中最直接最重要的影响因素之一. 假设通胀风险由服从几何布朗运动的物价指数来度量, 且瞬时期望通货膨胀率由Ornstein-Uhlenbeck过程来驱动. 金融市场由n+1种可连续交易的风险资产所构成, 养老基金管理者期望研究和解决通胀风险环境下DC型养老基金在累积阶段的最优投资策略问题, 以最大化终端真实财富过程的期望效用. 双曲绝对风险厌恶(HARA)效用函数具有一般的效用框架, 包含幂效用、指数效用和对数效用作为特例. 假设投资者对风险的偏好程度满足HARA效用, 运用随机最优控制理论和Legendre变换方法得到了最优投资策略的显式表达式.     

部分信息下带有保费返还条款的DC养老金时间一致性投资策略

本文研究了部分信息下带有保费返还条款的DC养老金的时间一致性投资策略.假设养老金管理者只拥有股票的部分信息,即只能观测到股票的价格,而不能观测到股票的收益率.养老金带有保费返还条款,在基金累积期死亡的参与者可以获得前期缴纳的所有保费.此外,本文还考虑了通胀风险以及随机工资.首先,利用卡尔曼滤波理论,将部分信息情形下的最优投资组合问题转化为一个完全信息情形下的问题.然后,通过求解一个扩展的HJB方程,得到时间一致性投资策略和最优值函数,并给出了均值–方差有效前沿的参数表达式.最后,用蒙特卡洛方法进行数值模拟,分析了部分信息和保费返还条款对股票投资比例和有效前沿的影响,并给出了相应的经济学解释.     

汇率风险和方差保费准则下最优投资和再保险策略

假定保险公司和再保险公司都采取方差保费准则收取保费,保险公司不但可以投资本国无风险资产和风险资产,还可以投资国外的风险资产.首先我们用一几何布朗运动来刻画汇率风险,同时为了控制保险风险,假定保险公司将承担的保险业务分保给再保险公司.接着利用随机动态规划原理研究了两种情形下的最优投资和再保险问题,一种是索赔服从扩散近似模型;另一种是经典风险模型,分别得到了这两种情形下的最优投资和再保险策略,并发现汇率风险对保险公司的投资策略有很大的影响,但对再保险策略没有影响.最后对相关参数进行了敏感性分析.     

随机利率环境下一类跳扩散相依风险资产的最优投资策略

考虑了随机利率环境下基于连续时间的动态最优资产配置问题。假设市场利率满足一个均值回复的随机过程,且金融市场由一个零息债券和两个价格受到共同冲击的相依性风险资产所构成。在均值-方差目标准则之下,利用随机最优控制理论和L agrange对偶原理获得了有效投资策略以及相应有效边界的解析式。最后通过数值算例,分析了有效策略及有效边界对相关参数的敏感性,并验证了相关理论结果。     

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.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

基于通货膨胀和最低保障的DC养老金最优投资

主要研究了通货膨胀和最低保障下的DC养老金的最优投资问题。 首先, 应用伊藤公式得到通胀折现后真实股票价格的微分方程。 然后, 在DC养老金终端财富外部保障约束下, 引入欧式看涨期权, 考虑随机通胀环境下的退休时刻终端财富期望效用最大化问题, 应用鞅方法推导退休时刻以及退休前任意时刻DC养老金最优投资策略的显式解。 最后, 应用蒙特卡洛方法对结果进行数值分析, 分析最低保障对DC养老金最优投资策略的影响。     

Optimal dynamic asset allocation of pension fund in mortality and salary risks framework

In this paper, we consider the optimal dynamic asset allocation of pension fund with mortality risk and salary risk. The managers of the pension fund try to find the optimal investment policy (optimal asset allocation) to maximize the expected utility of terminal wealth. The market is a combination of financial market and insurance market. The financial market consists of three assets: cashes with stochastic interest rate, stocks and rolling bonds, while the insurance market consists of mortality risk and salary risk. These two non-hedging risks cause incompleteness of the market. By martingale method and dynamic programming principle we first derive the approximate optimal investment policy to overcome the difficulty, then investigate the efficiency of the approximation. Finally, we solve an optimal assets liabilities management(ALM) problem with mortality risk and salary risk under CRRA utility, and reveal the influence of these two risks on the optimal investment policy by numerical illustration.     

Mean-variance optimization problems for an accumulation phase in a defined benefit plan

In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean-variance optimization problems, which are quadratic control problems with an additional constraint on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset whose price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies.     

随机环境下具有最低担保约束的DC养老金鲁棒投资策略

针对近年来养老金管理遇到的问题,基于模型不确定性,考虑随机环境和退休保障限制的DC型养老金最优投资策略具有重要意义.以养老金的最终价值相对于退休后年金担保的不变相对风险厌恶期望效用最大化为目标,利用随机动态规划的方法,求出鲁棒最优投资策略及相应的价值函数.最后,通过数值分析,得到各参数对最优投资策略的影响.     

Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model

In this paper, we study an optimal investment problem under the mean–variance criterion for defined contribution pension plans during the accumulation phase. To protect the rights of a plan member who dies before retirement, a clause on the return of premiums for the plan member is adopted. We assume that the manager of the pension plan is allowed to invest the premiums in a financial market, which consists of one risk-free asset and one risky asset whose price process is modeled by a jump–diffusion process. The precommitment strategy and the corresponding value function are obtained using the stochastic dynamic programming approach. Under the framework of game theory and the assumption that the manager’s risk aversion coefficient depends on the current wealth, the equilibrium strategy and the corresponding equilibrium value function are also derived. Our results show that with the same level of variance in the terminal wealth, the expected optimal terminal wealth under the precommitment strategy is greater than that under the equilibrium strategy with a constant risk aversion coefficient; the equilibrium strategy with a constant risk aversion coefficient is revealed to be different from that with a state-dependent risk aversion coefficient; and our results can also be degenerated to the results of He and Liang (2013b) and Björk et al. (2014). Finally, some numerical simulations are provided to illustrate our derived results.     

Nash equilibrium strategies for a defined contribution pension management

This paper studies the time-consistent investment strategy for a defined contribution (DC) pension plan under the mean–variance criterion. Since the time horizon of a pension fund management problem is relatively long, two background risks are taken into account: the inflation risk and the salary risk. Meanwhile, there are a risk-free asset, a stock and an inflation-indexed bond available in the financial market. The extended Hamilton–Jacobi–Bellman (HJB for short) equation of the equilibrium value function and the verification theorem corresponding to our problem are presented. The closed-form time-consistent investment strategy and the equilibrium efficient frontier are obtained by stochastic control technique. The effects of the inflation and stochastic income on the equilibrium strategy and the equilibrium efficient frontier are illustrated by mathematical and numerical analysis. Finally, we compare in detail the time-consistent results in our paper with the pre-commitment one and find the distinct properties of these two results.     

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.