Optimal dynamic asset allocation for pension funds in the presence of a minimum guarantee Marina Di Giacinto Universit`a degli studi di Cassino * Fausto Gozzi Libera Universit`a internazionale degli studi sociali “Guido Carli” - Roma Abstract In this paper we propose a continuous time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. Traditionally, portfolio selection models are interested in maximizing the total expected discounted utility from consumption and from final wealth, whereas our target is to maximize the total expected discounted utility from current wealth. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits, so that in general the portfolio is not self-financing and the level of wealth is constrained to stay above a “solvability level”. The fund manager can invest in a riskless asset and in a risky asset but borrowing and short selling are prohibited. Pension funds are exposed to financial and demographic risks, but in our model we consider these risks stochastically independent and we only analyze the financial aspects. Although this is the common assumption, it is questionable and we leave the inclusion of demographic risk to future research. Applying dynamic programming techniques, we discuss the existence, uniqueness and regu- larity of the value function which solves the related Hamilton-Jacobi-Bellman equation. Lastly we obtain the existence and uniqueness of the allocation strategy in a feedback form. Keywords: defined contribution pension fund, minimum guarantee, stochastic control problem, Hamilton-Jacobi-Bellman equation, viscosity solution. J.E.L. classification: C61, G11, G23. A.M.S. Subject Classification: 91B28, 93E20, 49L25. 1 Introduction This paper proposes to determine an optimal allocation of resources pertaining to a defined con- tribution pension fund with a minimum guarantee by dynamic programming techniques and by applying as control variable the proportion of wealth to invest in a risky asset. The first analysis on optimal selection portfolio in a continuous time model and using the dynamic programming approach was faced by R. C. Merton. Maximizing expected utility from * Corresponding author. Mailing address: Dipartimento Economia e territorio, Via Mazzaroppi, s.n.c., 03043 Cassino (FR), Italy. E-mail: digiacinto@unicas.it. 1