S (2007) Mean-variance optimization problems for an accumulation phase in a defined benefit plan

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 accu-mulated 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 liabil-ity 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 constrain 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 con-sists of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise, whereas the evolution of a mortality in-tensity 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