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Facelifting in utility maximization

Kasper Larsen (), Halil Mete Soner () and Gordan Žitković ()
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Kasper Larsen: Carnegie Mellon University
Halil Mete Soner: ETH
Gordan Žitković: University of Texas at Austin

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

Abstract: 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.

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