Optimal asset allocation for a DC plan with partial information under inflation and mortality risks

TL;DR

This paper develops a mathematical model for optimal asset allocation in a defined-contribution pension plan, considering inflation, mortality, and partial information, providing explicit solutions and a numerical example.

Contribution

It introduces a novel asset allocation framework incorporating inflation, mortality, and partial information, with closed-form solutions using a maximum principle approach.

Findings

Closed-form solutions for asset allocation under complex risks.

Inclusion of mortality and inflation risks in pension planning.

Numerical example demonstrating the model's application.

Abstract

We study an asset allocation stochastic problem with restriction for a defined-contribution pension plan during the accumulation phase. We consider a financial market with stochastic interest rate, composed of a risk-free asset, a real zero coupon bond price, the inflation-linked bond and the risky asset. A plan member aims to maximize the expected power utility derived from the terminal wealth. In order to protect the rights of a member who dies before retirement, we introduce a clause which allows to withdraw his premiums and the difference is distributed among the survival members. Besides the mortality risk, the fund manager takes into account the salary and the inflation risks. We then obtain closed form solutions for the asset allocation problem using a sufficient maximum principle approach for the problem with partial information. Finally, we give a numerical example.