Pension Funds with a Minimum Guarantee: A Stochastic Control Approach

Di Giacinto, Marina and Gozzi, Fausto and Salvatore, Federico (2008) Pension Funds with a Minimum Guarantee: A Stochastic Control Approach. [Working Paper]. Social Science Electronic Publishing. p. 44. SSRN Working Paper Series (In Press)

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In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. Usually, portfolio selection models for pension funds maximize the expected utility from final wealth over a finite horizon (the retirement time), whereas our target is to maximize the expected utility from current wealth over an infinite horizon since we adopt the point of view of the fund manager. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits and the level of wealth is constrained to stay above a solvency level. The fund manager can invest in a riskless asset and in a risky asset but borrowing and short selling are prohibited. We concentrate the analysis on the effect of the solvency constraint, analyzing in particular what happens when the fund wealth reaches the allowed minimum value represented by the solvency level. The model is naturally formulated as an optimal stochastic control problem and is treated by the dynamic programming approach. We show that the value function of the problem is a regular solution of the associated Hamilton-Jacobi-Bellman equation. Then we apply verification techniques to get the optimal allocation strategy in feedback form and to study its properties. We finally give a special example with explicit solution.

Item Type: Report / Paper (Working Paper)
Research documents and activity classification: Working Papers > Refereed Working Papers / of international relevance
Divisions: Department of Business and Management
Additional Information: The paper is forthcoming in "Finance and Stochastics"
Uncontrolled Keywords: Defined contribution pension fund, minimum guarantee, stochastic optimal control, dynamic programming, Hamilton-Jacobi-Bellman equation, viscosity solutions
MIUR Scientific Area: Area 13 - Economics and Statistics > SECS-S/06 Mathematics for Economics, Actuarial Studies and Finance
Deposited by: Maria Teresa Nisticò
Date Deposited: 02 Dec 2010 15:29
Last Modified: 22 Apr 2015 00:13


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