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Mean-variance optimization problems for an accumulation phase in a defined benefit plan

Delong, L., Gerrard, R. J. G. and Haberman, S. (2008). Mean-variance optimization problems for an accumulation phase in a defined benefit plan. Insurance: Mathematics and Economics, 42(1), pp. 107-118. doi: 10.1016/j.insmatheco.2007.01.005


In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean–variance optimization problems, which are quadratic control problems with an additional constraint on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset whose price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Insurance: Mathematics and Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Insurance: Mathematics and Economics, Volume 42, Issue 1, February 2008, Pages 107–118,
Publisher Keywords: Lévy diffusion financial market; Stochastic mortality intensity process; Hamilton–Jacobi–Bellman equation; Feynman–Kac representation
Subjects: H Social Sciences > HF Commerce
Departments: Cass Business School > Actuarial Science & Insurance
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