Constrained Portfolio Choices in the Decumulation Phase of a Pension Plan

Di Giacinto, Marina and Salvatore, Federico and Gozzi, Fausto and Vigna, Elena (2010) Constrained Portfolio Choices in the Decumulation Phase of a Pension Plan. [Working Paper]. p. 54. Carlo Alberto Notebooks (No. 155).

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This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement. This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. The main goal is to find the optimal portfolio choice to be adopted by the retiree from retirement to annuitization time in a Black and Scholes financial market. We define and study the problem at two different complexity levels. In the first level (problem P1), we only require no short-selling. In the second level (problem P2), we add a constraint on the state variable, by imposing that the final fund cannot be lower than a certain guaranteed safety level. This implies, in particular, no ruin. The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We give a general result of existence and uniqueness of regular solutions for the Hamilton-Jacobi-Bellman equation and, in a special case, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application of the special case - when explicit solutions are available - ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.

Item Type: Report / Paper (Working Paper)
Research documents and activity classification: Working Papers > Non-Refereed Working Papers / of national relevance only
Divisions: Department of Business and Management
Uncontrolled Keywords: pension fund, decumulation phase, constrained portfolio, Stochastic optimal control, dynamic programming, Hamilton-Jacobi-Bellman equation.
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 16:40
Last Modified: 21 Apr 2015 23:13


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