基于Heston模型的待遇预定制养老基金管理最优决策

资产组合与缴费计划是待遇预定制养老基金管理的核心问题.针对此类养老基金的管理,建立Heston随机波动率模型,结合最优控制理论和Legendre变换,将原问题转化为对偶问题,通过对偶问题的求解,求得原问题的解析解,从而确定风险资产比例和缴费水平,最终实现养老基金管理的最优资产配置和最低缴费水平.     

固定支出下最优资产组合策略

在固定消费支出水平的条件之下,文章就资产组合问题建立常方差弹性（CEV）模型,应用随机控制原理求出了相应的非线性Hamilton—Jacobi—Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题。通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果．     

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.     

多目标分式规划逆对偶研究

考虑了一类可微多目标分式规划问题.首先,建立原问题的两个对偶模型.随后,在相关文献的弱对偶定理基础上,利用Fritz John型必要条件,证明了相应的逆对偶定理.     

非仿射随机波动率的欧式障碍期权定价

研究非仿射随机波动率模型的欧式障碍期权定价问题时,首先介绍了非仿射随机波动率模型,其次利用投资组合和It^o引理,得到了该模型下扩展的Black-Schole偏微分方程.由于这个方程没有显示解,因此采用对偶蒙特卡罗模拟法计算欧式障碍期权的价格.最后,通过数值实例验证了算法的可行性和准确性.     

中国城乡居民养老制度可持续性的精算研究

围绕我国城乡居民养老保险体系可持续化问题,从中国实际出发,分层次、多角度的分析了当前我国的养老保险制度.首先,针对中国养老保险基金问题,基于当前养老保险体制,分别从三个层次入手,建立中国城乡居民养老保险基金收支模型;其次,基于养老制度的可持续性,建立了养老金缺口模型,并对养老金缺口的未来趋势进行了合理预测;最后,对所建立的模型进行了评价及推广.     

一类锥约束多目标优化问题的高阶对偶研究

在一类锥约束单目标优化问题的一阶对偶模型基础之上,建立了锥约束多目标优化问题的二阶和高阶对偶模型.在广义凸性假设下,给出了弱对偶定理,在Kuhn-Tucker约束品性下,得到了强对偶定理.最后,在弱对偶定理的基础上,利用Fritz-John型必要条件建立了逆对偶定理.     

养老基金投资组合的常方差弹性(CEV)模型和解析决策

针对以年金形式发放待遇的缴费预定制养老基金，在退休前和退休后的两个阶段，分别构建了常方差弹性（CEV）模型，并应用Legendre变换将原问题转化为对偶问题，在追求指数效用最大化的条件下，求得了精确解析解，从而确定了这两个阶段的最优投资决策．     

贷款组合的“均值-方差-偏度”三因素优化模型

以银行各项资产组合收益率最大化为目标函数,以收益率偏度大于零控制银行重大损失发生的概率,以组合风险价值VaR风险限额为约束条件控制资产组合风险的大小,建立了贷款组合的"均值-方差-偏度"三因素优化模型.本模型的创新与特色一是通过偏度约束减少了组合收益率小于其均值的可能性,并增加了组合收益率大于其均值的概率.这在均值-方差模型的基础上,增加了偏度参数,建立了收益率均值-方差-偏度模型,开拓了资产组合优化的新思路.二是以组合风险价值VaR建立了约束条件,通过在一定置信水平下的最大损失限额来制约贷款组合的违约风险,使贷款配给的风险限定在银行的承受能力和贷款准备金的范围之内,解决了整体风险的控制问题.     

广义向量变分不等式和广义对偶模型

研究实Banach空间中带有不等式约束的非光滑向量优化问题(VP).首先,借助下方向导数引进了广义Minty型向量变分不等式,并通过变分不等式来探讨问题(VP)的最优性条件.接着,利用函数的上次微分构造了不可微向量优化问题(VP)的广义对偶模型,并且在适当的弱凸性条件下建立了弱对偶定理.     

A benchmarking approach to optimal asset allocation for insurers and pension funds

We solve the optimal asset allocation problem for an insurer or pension fund by using a benchmarking approach. Under this approach the objective is an increasing function of the relative performance of the asset portfolio compared to a benchmark. The benchmark can be, for example, a function of an insurer’s liability payments, or the (either contractual or target) payments of a pension fund. The benchmarking approach tolerates but progressively penalizes shortfalls, while at the same time progressively rewards outperformance. Working in a general, possibly non-Markovian setting, a solution to the optimization problem is presented, providing insights into the impact of benchmarking on the resulting optimal portfolio. We further illustrate the results with a detailed example involving an option based benchmark of particular interest to insurers and pension funds, and present closed form solutions.     

Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model

This paper considers an optimal investment problem for a defined contribution (DC) pension plan with default risk in a mean–variance framework. In the DC plan, contributions are supposed to be a predetermined amount of money as premiums and the pension funds are allowed to be invested in a financial market which consists of a risk-free asset, a defaultable bond and a risky asset satisfied a constant elasticity of variance (CEV) model. Notice that a part of pension members could die during the accumulation phase, and their premiums should be withdrawn. Thus, we consider the return of premiums clauses by an actuarial method and assume that the surviving members will share the difference between the return and the accumulation equally. Taking account of the pension fund size and the volatility of the accumulation, a mean–variance criterion as the investment objective for the DC plan can be formulated, and the original optimization problem can be decomposed into two sub-problems: a post-default case and a pre-default case. By applying a game theoretic framework, the equilibrium investment strategies and the corresponding equilibrium value functions can be obtained explicitly. Economic interpretations are given in the numerical simulation, which is presented to illustrate our results.     

Pension funding problem with regime‐switching geometric Brownian motion assets and liabilities

This paper extends the pension funding model in (N. Am. Actuarial J. 2003; 7 :37–51) to a regime‐switching case. The market mode is modeled by a continuous‐time stationary Markov chain. The asset value process and liability value process are modeled by Markov‐modulated geometric Brownian motions. We consider a pension funding plan in which the asset value is to be within a band that is proportional to the liability value. The pension plan sponsor is asked to provide sufficient funds to guarantee the asset value stays above the lower barrier of the band. The amount by which the asset value exceeds the upper barrier will be paid back to the sponsor. By applying differential equation approach, this paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In addition, we study the effects of different barriers and regime switching on the results using some numerical examples. The optimal dividend problem is studied in our examples as an application of our theory. Copyright © 2009 John Wiley & Sons, Ltd.     

Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework

This paper investigates an asset allocation problem for defined contribution pension funds with stochastic income and mortality risk under a multi-period mean–variance framework. Different from most studies in the literature where the expected utility is maximized or the risk measured by the quadratic mean deviation is minimized, we consider synthetically both to enhance the return and to control the risk by the mean–variance criterion. First, we obtain the analytical expressions for the efficient investment strategy and the efficient frontier by adopting the Lagrange dual theory, the state variable transformation technique and the stochastic optimal control method. Then, we discuss some special cases under our model. Finally, a numerical example is presented to illustrate the results obtained in this paper.     

Designing and pricing guarantee options in defined contribution pension plans

The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. However, for DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio and we develop a discrete model that selects the reference portfolio to minimize the cost of a guarantee. While the relation DB–DC is typically viewed as a binary one, the model shows how to price a wide range of guarantees creating a continuum between DB and DC. Integrating guarantee pricing with asset allocation decision is useful to both pension fund managers and regulators. The former are given a yardstick to assess if a given asset portfolio is fit-for-purpose; the latter can assess differences of specific reference funds with respect to the optimal one, signaling possible cases of moral hazard. We develop the model and report numerical results to illustrate its uses.     

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.     

On “optimal pension management in a stochastic framework” with exponential utility

This paper reconsiders the optimal asset allocation problem in a stochastic framework for defined-contribution pension plans with exponential utility, which has been investigated by Battocchio and Menoncin [Battocchio, P., Menoncin, F., 2004. Optimal pension management in a stochastic framework. Insurance: Math. Econ. 34, 79-95]. When there are three types of asset, cash, bond and stock, and a non-hedgeable wage risk, the optimal pension portfolio composition is horizon dependent for pension plan members whose terminal utility is an exponential function of real wealth (nominal wealth-to-price index ratio). With market parameters usually assumed, wealth invested in bond and stock increases as retirement approaches, and wealth invested in cash asset decreases. The present study also shows that there are errors in the formulation of the wealth process and control variables in solving the optimization problem in the study of Battocchio and Menoncin, which render their solution erroneous and lead to wrong results in their numerical simulation.