Optimal Portfolio Strategies with Stochastic Wage Income and Inflation: The Case of a Defined Contribution Pension Plan
AbstractWe consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market with stochastic interest rate. The fund manager must cope with a set of stochastic investment opportunities and two background risks: the salary risk and the inflation risk. We use the stochastic dynamic programming approach. We show that the presence of the inflation risk can solve some problems linked to the use of the stochastic dynamic programming technique, and namely to the stochastic partial differential equation deriving from it. We find a closed form solution to the asset allocation problem, without specifying any functional form for the coe±cients of the diffusion processes involved in the problem. Finally, the derivation of a closed form solution allows us to analyse in detail the behaviour of the optimal portfolio with respect to salary and inflation.
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Bibliographic InfoPaper provided by Center for Research on Pensions and Welfare Policies, Turin (Italy) in its series CeRP Working Papers with number 19.
Length: 28 pages
Date of creation: Mar 2002
Date of revision:
defined-contribution pension plan; salary risk; inflation risk; stochastic optimal control; Hamilton-Jacobi-Bellman equation;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
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- Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
- Paolo BATTOCCHIO & Francesco MENONCIN, 2002. "Optimal Pension Management under Stochastic Interest Rates, Wages, and Inflation," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), UniversitÃ© catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2002021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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