Abstract
This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that the financial market consists of a risk-free asset and a risky asset, where the risky asset is subject to the Ornstein–Uhlenbeck (O-U) process, and stochastic income and inflation risk were also considered in the model. We firstly derived the Hamilton–Jacobi–Bellman (HJB) equation through the stochastic control method. Secondly, under the logarithmic utility function, the closed-form solution of optimal asset allocation was obtained by using the Legendre transform method. Finally, we give several numerical examples and a financial analysis.
Highlights
With the increase of the elderly population, the investment problem of the current endowment insurance system is a hot issue
Vigna and Haberman [1] put forward the discrete pension for the first time, and the dynamic programming method was applied to the optimal investment strategy of the defined contribution (DC) pension plan
Gu et al [22] assumed that the risky asset price meets the O-U model and studied the optimal investment problem of the DC pension plan when the pension manager’s preference is the power utility function
Summary
With the increase of the elderly population, the investment problem of the current endowment insurance system is a hot issue. Li et al [12] considered an optimal investment problem for a defined contribution pension plan with default risk in a mean-variance framework under a CEV model. The member has a stochastic salary, considers inflation risk, and invests his/her pension account wealth into a financial market consisting of a riskfree asset, an inflation-indexed bond, and a stock whose expected return rate follows a mean-reverting process. Gu et al [22] assumed that the risky asset price meets the O-U model and studied the optimal investment problem of the DC pension plan when the pension manager’s preference is the power utility function. To incorporate inflation risk into the DC pension plan, we assumed that financial market consists of a risk-free asset and a risky asset, where the risky asset is subject to the O-U process and the stochastic income is considered in the model.
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