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Facelifting in utility maximization

Kasper Larsen (), Halil Soner () and Gordan Žitković ()

Finance and Stochastics, 2016, vol. 20, issue 1, 99-121

Abstract: We establish the existence and characterization of a primal and a dual facelift—discontinuity of the value function at the terminal time—for utility maximization in incomplete semimartingale-driven financial markets. Unlike in the lower and upper hedging problems, and somewhat unexpectedly, a facelift turns out to exist in utility maximization despite strict convexity in the objective function. In addition to discussing our results in their natural, Markovian environment, we also use them to show that the dual optimizer cannot be found in the set of countably additive (martingale) measures in a wide variety of situations. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: Boundary layer; Convex analysis; Convex duality; Facelift; Financial mathematics; Incomplete markets; Markov processes; Utility maximization; Unspanned endowment; 91G10; 91G80; 60K35; C61; G11 (search for similar items in EconPapers)
Date: 2016
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