带遗产计划和非流动性资产的DC型养老金的最优投资组合问题

Optimal Portfolio Problem for a DC Pension Plan with Estate Planning and Illiquid Assets

摘要: 本文探讨了当缴费确定(DC)型养老金计划考虑非流动性资产投资时的最优投资组合问题，并研究非流动性对投资组合选择的影响，同时还涉及养老金计划参与者的遗产计划、退休前随机劳动工资、退休后的生活保障和通货膨胀的风险。建模时，假设投资者可投资于无风险资产、股票和指数债券外，还有一种非流动性资产，我们考虑一个定期投资，即只能在时间0时进行交易，并在退休时提供回报。投资者同时表现出寻求风险和厌恶损失的行为，退休时投资回报的效用为S型。我们首先应用Legendre-Fenchel变换得到最优终端财富，然后采用鞅方法得到完整市场中最优投资策略和财富过程，并给出非流动性资产的最优交易策略，解决了投资者的最优投资组合问题。在此基础上，结合一些数字结论来分析模型参数和一些特征对投资策略的影响。

Abstract: This paper explores the optimal portfolio problem when a defined contribution (DC) pension plan considers investments in illiquid assets and examines the impact of illiquidity on portfolio choice, as well as the risks of estate planning, stochastic pre-retirement labor wages, post-retirement living security, and inflation for pension plan participants. For modeling, it is assumed that an investor can invest in an illiquid asset in addition to risk-free assets, stocks and indexed bonds, and we con-sider a periodic investment that can only be traded at time 0 and provides returns at retirement. The investor exhibits both risk-seeking and loss averse behavior, and the S-shaped utility from the investment return at retirement. We first apply the Legendre-Fenchel transformation to obtain the optimal terminal wealth, and then use the harnessing method to obtain the optimal investment strategy and wealth process in the complete market, and give the optimal trading strategy for illiq-uid assets, which solves the optimal portfolio problem for investors. On this basis, some numerical conclusions are combined to analyze the effects of model parameters and some features on invest-ment strategies.