A general optimization framework for the annuity contracts with multiscale stochastic volatility

Yong Hong Wu,Yan Zhang

doi:10.1080/23311835.2017.1385375

Abstract

This paper develops the annuity contract model in the presence of multiscale stochastic volatility for studying the optimal investment strategy before and after retirement in a defined contribution...

Highlights

There are two main types of pension funds: defined benefit (DB) pension fund and defined contribution (DC) pension fund
We study an annuity model in the context of a DC pension fund management and derive optimal investment strategy for both accumulation stage and distribution stage
The optimization management problem for the annuity contract with multiscale stochastic volatility (MSSV) refers to the problem of finding the optimal investment strategy such that the utility function for the insurer is maximized

Summary

Introduction

There are two main types of pension funds: defined benefit (DB) pension fund and defined contribution (DC) pension fund. We study an annuity model in the context of a DC pension fund management and derive optimal investment strategy for both accumulation stage and distribution stage. Asset allocation optimization problem of annuity/DC pension fund management has drawn more and more attention of talented researchers, many of which have contributed high quality research output. Most of these research works assume that the volatility of the risky asset price is constant, time-dependent function, or follow the CEV model. The insurer manages the pension fund and accumulates wealth by investing in financial market. During [T, T + N], the insurer pays out benefits and invests its wealth in the financial market with one risk-free asset and one risky asset.

Optimization problem

General framework before retirement We define the value function as follows

General framework after retirement We define the value function as follows

Conclusions