Wealth-Path Dependent Utility Maximization in Incomplete Markets
Bouchard, Bruno; Pham, Huyen (2004), Wealth-Path Dependent Utility Maximization in Incomplete Markets, Finance and Stochastics, 8, 4, p. 579-603. http://dx.doi.org/10.1007/s00780-004-0125-8
TypeArticle accepté pour publication ou publié
Journal nameFinance and Stochastics
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Abstract (EN)Motivated by an optimal investment problem under time horizon uncertainty and when default may occur, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth-path dependent utility maximization problem. Our main result is an extension of the well-known dual formulation to this context. In contrast with the usual duality approach, we work directly on the primal problem. Sufficient conditions for characterizing the optimal solution are also provided in the case of complete markets, and are illustrated by examples.
Subjects / Keywordsrandom time horizon; incomplete markets; convex duality; Mathematical Finance; Utility maximization
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