Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1301.0280.
Date of creation: Jan 2013
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-12 (All new papers)
- NEP-MIC-2013-01-12 (Microeconomics)
- NEP-UPT-2013-01-12 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2010. "Constrained portfolio choices in the decumulation phase of a pension plan," Carlo Alberto Notebooks 155, Collegio Carlo Alberto.
- Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
- Bruno Bouchard & HuyÃªn Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
- Eduardo S. Schwartz & Claudio Tebaldi, 2006. "Illiquid Assets and Optimal Portfolio Choice," NBER Working Papers 12633, National Bureau of Economic Research, Inc.
- Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
- Bouchard, Bruno & Pham, Huyen, 2004. "Wealth-Path Dependent Utility Maximization in Incomplete Markets," Economics Papers from University Paris Dauphine 123456789/1803, Paris Dauphine University.
- Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2012. "Impact of time illiquidity in a mixed market without full observation," Papers 1211.1285, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.