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. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. 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 with state constraints 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.

Pension Funds with a Minimum Guarantee: A Stochastic Control Approach / DI GIACINTO, M; Federico, S; Gozzi, Fausto. - In: FINANCE AND STOCHASTICS. - ISSN 0949-2984. - 15:2(2011), pp. 297-342. [10.1007/s00780-010-0127-7]

Pension Funds with a Minimum Guarantee: A Stochastic Control Approach

GOZZI, FAUSTO
2011

Abstract

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. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. 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 with state constraints 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.
Defined contribution pension fund, Minimum guarantee, Stochastic optimal control, Dynamic programming, Hamilton–Jacobi–Bellman equation, Viscosity solution,
Pension Funds with a Minimum Guarantee: A Stochastic Control Approach / DI GIACINTO, M; Federico, S; Gozzi, Fausto. - In: FINANCE AND STOCHASTICS. - ISSN 0949-2984. - 15:2(2011), pp. 297-342. [10.1007/s00780-010-0127-7]
File in questo prodotto:
File Dimensione Formato  
art%3A10.1007%2Fs00780-010-0127-7.pdf

Solo gestori archivio

Tipologia: Versione dell'editore
Licenza: Tutti i diritti riservati
Dimensione 1.26 MB
Formato Adobe PDF
1.26 MB Adobe PDF   Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/3638
Citazioni
  • Scopus 48
  • ???jsp.display-item.citation.isi??? 42
social impact