Backward Stochastic PDEs Related to the Utility Maximization Problem

Michael Mania () and Revaz Tevzadze ()

ICER Working Papers - Applied Mathematics Series from ICER - International Centre for Economic Research

Abstract: We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As examples the cases of power, exponential and logarithmic utilities are considered

Keywords: Backward stochastic partial di erential equation; utility maximization problem; semimartingale; incomplete markets (search for similar items in EconPapers)
Pages: 25 pages
Date: 2008-06
New Economics Papers: this item is included in nep-dge and nep-upt
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Citations: View citations in EconPapers (8)

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