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Dual formulation of the utility maximization problem: the case of nonsmooth utility. (English) Zbl 1126.91018

Summary: We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results [see e.g. M. P. Owen, Ann. Appl. Probab. 12, No. 2, 691–709 (2002; Zbl 1049.91082)] in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the shortfall minimization problems in our framework. Second, we allow for the presence of some given liability or a random endowment. In particular, these results provide a dual formulation of the utility indifference valuation rule.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
91B28 Finance etc. (MSC2000)
49J52 Nonsmooth analysis
49N15 Duality theory (optimization)
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B62 Economic growth models
93E20 Optimal stochastic control
91B16 Utility theory

Citations:

Zbl 1049.91082
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References:

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