Thispaperdealswithaninvestment–consumptionportfolioproblemwhen the current utility depends also on the wealth process. Such problems arise e.g. in portfolio optimization with random horizon or random trading times. To overcome the difficulties of the problem, a dual approach is employed: a dual control problem is defined and treated by means of dynamic programming, showing that the viscos- ity solutions of the associated Hamilton–Jacobi–Bellman equation belong to a suit- able class of smooth functions. This allows defining a smooth solution of the primal Hamilton–Jacobi–Bellman equation, and proving by verification that such a solution is indeed unique in a suitable class of smooth functions and coincides with the value function of the primal problem. Applications to specific financial problems are given.

Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation / S. Federico, P. Gassiat, F. Gozzi. - In: FINANCE AND STOCHASTICS. - ISSN 0949-2984. - 19:2(2015 Apr), pp. 415-448. [10.1007/s00780-015-0257-z]

Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation

S. Federico
Primo
;
2015

Abstract

Thispaperdealswithaninvestment–consumptionportfolioproblemwhen the current utility depends also on the wealth process. Such problems arise e.g. in portfolio optimization with random horizon or random trading times. To overcome the difficulties of the problem, a dual approach is employed: a dual control problem is defined and treated by means of dynamic programming, showing that the viscos- ity solutions of the associated Hamilton–Jacobi–Bellman equation belong to a suit- able class of smooth functions. This allows defining a smooth solution of the primal Hamilton–Jacobi–Bellman equation, and proving by verification that such a solution is indeed unique in a suitable class of smooth functions and coincides with the value function of the primal problem. Applications to specific financial problems are given.
Optimal stochastic control; Investment–consumption problem; Duality; Hamilton–Jacobi–Bellman equation; Regularity of viscosity solutions
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore MAT/05 - Analisi Matematica
apr-2015
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/263564
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