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

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

Papers from arXiv.org

**Abstract:**
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random trading times. To overcome the difficulties of the problem we use the dual approach. We define a dual problem and treat it 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 to define a smooth solution of the primal Hamilton-Jacobi-Bellman equation, proving that this solution is indeed unique in a suitable class and coincides with the value function of the primal problem. Some financial applications of the results are provided.

**New Economics Papers:** this item is included in nep-mic and nep-upt

**Date:** 2013-01, Revised 2015-02

**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://arxiv.org/pdf/1301.0280 Latest version (application/pdf)

**Related works:**

Journal Article: 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:arx:papers:1301.0280

Access Statistics for this paper

More papers in Papers from arXiv.org

Series data maintained by arXiv administrators ().