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| Type | Working Paper |
| Scope | Discipline-based scholarship |
| Title | Utility Maximization with a Given Pricing Measure When the Utility Is Not Necessarily Concave |
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| Series Name | NCCR FINRISK Working Paper |
| Number | 517 |
| Date | 2011 |
| Abstract Text | We study the problem of maximizing expected utility from terminal wealth for a non-concave utility function and for a budget set given by one fixed pricing measure. We prove the existence of a maximizer and show that the concave envelope of the (non-concave) value function (indirect utility) is the value function of the utility maximization problem for the concave envelope of the original utility function. The value functions are shown to coincide if the underlying probability space is atomless. For a converging sequence of models, we prove that the sequence of value functions and a subsequence of optimal allocations converge to the corresponding quantities in the limit model. We illustrate our results by concrete numerical examples. |
| Official URL | http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1940277 |
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