基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置

本文从养老金计划参与人和基金经理的双重视角出发,以最大化双方加权的期望效用为目标,研究了在最低保障和VaR约束下,DC养老金计划的最优资产配置问题。假设养老金计划参与人和基金经理均是损失厌恶的,分别用两个S型的效用函数来刻画双方的损失厌恶行为。VaR约束和加权的效用函数使得本文所研究的优化问题成为一个复杂的非凹效用最大化问题。利用拉格朗日对偶理论和凹化方法求得了最优财富和最优投资组合的封闭解。数值结论表明当更为看重养老金计划参与人的利益时,基金经理会采取更为激进的投资策略,VaR约束可以改进对DC养老金计划的风险管理。     

激励机制和VaR约束下的DC养老金计划的最优投资

研究了DC养老金经理在单一管理费以及混合收费(同时收取管理费与绩效费)这两种不同的薪酬机制和损失厌恶下的最优投资组合问题。利用凹化方法得到了存在终端财富约束下的最优财富过程和最优投资策略的解析表达式。数值结果表明损失厌恶,VaR约束和薪酬机制会极大地影响最优终端财富的分布。特别地,在决策参照点较高时,损失厌恶会导致混合薪酬机制下最优终端财富的尾部风险较低。     

Optimal portfolio choice for an insurer with loss aversion

The problem of optimal investment for an insurance company attracts more attention in recent years. In general, the investment decision maker of the insurance company is assumed to be rational and risk averse. This is inconsistent with non fully rational decision-making way in the real world. In this paper we investigate an optimal portfolio selection problem for the insurer. The investment decision maker is assumed to be loss averse. The surplus process of the insurer is modeled by a Lévy process. The insurer aims to maximize the expected utility when terminal wealth exceeds his aspiration level. With the help of martingale method, we translate the dynamic maximization problem into an equivalent static optimization problem. By solving the static optimization problem, we derive explicit expressions of the optimal portfolio and the optimal wealth process.     

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.     

Heston模型下DC型养老金鲁棒最优投资问题

本文研究在随机工资和模型不确定性影响下确定缴费型养老金的鲁棒最优投资问题. 在模型中,养老金账户中的资本可以投资于一种风险资产和一种无风险资产,假设风险资产价格满足Heston模型. 研究目标是通过选择最优投资策略,使得养老金账户的终端相对财富效用最大化. 利用随机动态规划的方法,我们求出了在幂效用函数和指数效用函数下鲁棒最优投资策略和相应的值函数.最后, 通过MATLAB软件对理论结果进行了数值分析.     

不完全信息和模糊厌恶下DC型养老金最优投资策略

在信息部分可观测的金融市场中,参与者可投资于一个无风险资产、一个滚动债券和一支股票。其中,股票的预期收益率由一个服从均值-回复过程的预测因子预测。参与者是模糊厌恶的,只能观测到股票价格和利率,却无法观测到预测因子。利用滤波技术和动态规划原理,得到了不完全信息和模糊厌恶下DC型养老金最优投资策略的解析式。进一步,利用敏感性分析和比较静态分析,对比仅考虑不完全信息、仅考虑模糊厌恶以及同时考虑不完全信息和模糊厌恶三种情形下的最优投资策略。结果表明同时考虑不完全信息和模糊厌恶时的最优投资策略最保守,仅考虑不完全信息时的最优投资策略对风险厌恶系数的变化最敏感。     

基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

研究了确定缴费型养老基金在退休前累积阶段的最优资产配置问题.假设养老基金管理者将养老基金投资于由一个无风险资产和一个价格过程满足Stein-Stein随机波动率模型的风险资产所构成的金融市场.利用随机最优控制方法,以最大化退休时刻养老基金账户相对财富的期望效用为目标,分别获得了无约束情形和受动态VaR (Value at Risk)约束情形下该养老基金的最优投资策略,并获得相应最优值函数的解析表达形式.最后通过数值算例对相关理论结果进行数值验证并考察了最优投资策略关于相关参数的敏感性.     

A new defined benefit pension risk measurement methodology

Defined benefit pension plan sponsors have taken on greater risks for sponsoring these plans in the last several years. Due to ever increasing concerns of longevity risk and the weak economic environment, sponsors are eager to understand their pension-related risks to facilitate optimal enterprise decision-making. Borrowing an analytical framework from the life insurance and annuity industry where the amount of risk is framed in terms of the total assets required to remain solvent over a one-year period with a high level of confidence, i.e., the economic capital approach, this paper develops a benchmark risk measure for pension sponsors by obtaining a total asset requirement for sustaining the pension plan. The difference between the total asset requirement and the actual trust assets thus provides a measure of sponsor assets at risk due to plan sponsorship. Two factor-based approaches are proposed for this calculation. The first approach develops a set of pension-specific factors as if the pension plan were a group annuity. The second approach directly simulates the risk drivers of the pension plan and develops a framework for obtaining factors and calculating the pension risk given a desired confidence level. Our approach is very easy to implement and monitor in practice.     

带随机工资的目标收益养老金计划的鲁棒最优投资和收益支付调整策略

本文在目标收益计划(TBPs)下考虑了具有违约风险和模型不确定性的最优投资和收益支付问题。养老金可以投资到无风险资产, 价格服从Heston模型的股票和违约债券。特别地, TBPs成员的工资是随机的。利用随机最优控制方法, 分别推导出了违约后和违约前的鲁棒最优策略和相应的值函数。此外, 还考虑了模糊中性情况下的最优策略。最后给出数值分析来说明参数对最优策略的影响, 从而为养老金管理者提供了有效的决策依据。     

Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework

We solve a mean–variance optimisation problem in the accumulation phase of a defined contribution pension scheme. In a general multi-asset financial market with stochastic investment opportunities and stochastic contributions, we provide the general forms for the efficient frontier, the optimal investment strategy, and the ruin probability. We show that the mean–variance approach is equivalent to a “user-friendly” target-based optimisation problem which minimises a quadratic loss function, and provide implementation guidelines for the selection of the target. We show that the ruin probability can be kept under control through the choice of the target level. We find closed-form solutions for the special case of stochastic interest rate following the Vasiček (1977) dynamics, contributions following a geometric Brownian motion, and market consisting of cash, one bond and one stock. Numerical applications report the behaviour over time of optimal strategies and non-negative constrained strategies.     

基于跳扩散模型的DC型 养老金时间一致最优投资策略的研究

将养老金投资过程分成财富积累阶段和财富给付阶段,建立了DC型养老金在退休前和退休后个人账户积累额变动的连续时间随机模型.该模型考虑了工资的随机风险因素,并用跳扩散模型刻画风险资产.以均值方差准则作为优化目标,运用推广的HJB方程分别得到了退休前和退休后的时间一致最优风险资产投资最优解.最后通过算例及敏感性分析研究了各个...     

Loss reserving using loss aversion functions

This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies, and extends existing disparate approaches discussed in the literature. Analytical and computer generated illustrations are given as well as suggestions for the practical determination of aversion functions.