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

*Salvatore Federico*,
*Paul Gassiat* () and
*Fausto Gozzi*

*Finance and Stochastics*, 2015, vol. 19, issue 2, 415-448

**Abstract:**
This paper deals with an investment–consumption portfolio problem when 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 viscosity solutions of the associated Hamilton–Jacobi–Bellman equation belong to a suitable 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. Copyright Springer-Verlag Berlin Heidelberg 2015

**Keywords:** Optimal stochastic control; Investment–consumption problem; Duality; Hamilton–Jacobi–Bellman equation; Regularity of viscosity solutions; 93E20; 49L20; 90C46; 91G80; 35B65; C61; G11 (search for similar items in EconPapers)

**Date:** 2015

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** View citations in EconPapers (2) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1007/s00780-015-0257-z (text/html)

Access to full text is restricted to subscribers.

**Related works:**

Working Paper: Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation (2015)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:spr:finsto:v:19:y:2015:i:2:p:415-448

**Ordering information:** This journal article can be ordered from

http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by *M. Schweizer*

More articles in Finance and Stochastics from Springer

Bibliographic data for series maintained by Sonal Shukla ().