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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1301.0280.
Date of creation: Jan 2013
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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)
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