DYNAMIC HEDGING OF THE MORTALITY RISK VIA A CONTINUOUS CONTROL STRATEGY OF THE PORTFOLIO OF INVESTMENTS OF A PENSION FUND

Alexandros A. Zimbidis (Greece) and Athanasios A. Pantelous (Greece)

Received October 23, 2007

Abstract

In this paper, we propose and model a realistic approach for the management of a defined contribution pension scheme in the distribution phase (post-retirement period) providing a whole life assurance benefit. We assume a stochastic framework for both mortality and investment risk and additionally suggest a correlation effect between the two separate risks. By using the HJB equation, we design a concrete solution with respect to the optimal investment strategy and the optimal rate of death benefit payments. The final formulae, although complicated, provide a deep insight into the mechanisms of the management’s decisions. They also coincide with classical approaches and solutions from the finance field.

Keywords and phrases: pension fund, whole life assurance, optimal control theory, HJB equation.