In this paper we propose and study a continuous time stochastic model of optimal al- location for a defined contribution pension fund in the accumulation phase. 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. The model is naturally formu- lated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach. We show that the value function of the problem is a continuous viscosity solution of the associated Hamilton-Jacobi-Bellman equation. In the special case when the bound- ary is absorbing we show that it is the unique viscosity solution of the Hamilton-Jacobi-Bellman equation

A Pension Fund Model in the Accumulation Phase: a Stochastic Control Approach / S. Federico - In: Advances in Mathematics of Finance[s.l] : Banach center publications, 2008. - pp. 61-83 (( convegno AMAMEF conference tenutosi a Bedlewo, Polonia nel 2007.

### A Pension Fund Model in the Accumulation Phase: a Stochastic Control Approach

#### Abstract

In this paper we propose and study a continuous time stochastic model of optimal al- location for a defined contribution pension fund in the accumulation phase. 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. The model is naturally formu- lated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach. We show that the value function of the problem is a continuous viscosity solution of the associated Hamilton-Jacobi-Bellman equation. In the special case when the bound- ary is absorbing we show that it is the unique viscosity solution of the Hamilton-Jacobi-Bellman equation
##### Scheda breve Scheda completa Scheda completa (DC)
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/06 - Probabilita' e Statistica Matematica
2008
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/211919`