Maximization of Non-Concave Utility Functions in Discrete-Time Financial Market Models

2013/02/01 by Laurence Carassus, Carassus, Laurence, Miklos Rasonyi +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #28B20 #91B16 Secondary 91G10 #91B70 #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Primary 93E20 #math.OC #msc:28B20 #msc:91B16 #msc:91B70 #msc:91G10 #msc:93E20 #q-fin.PM

paper · pdf · doi:10.48550/arxiv.1302.0134

Second revision

arxiv created 2014/09/03 · arxiv updated 2014/09/04

Abstract

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility function U is considered, with domain of definition ℝ. Simple conditions are presented which guarantee the existence of an optimal strategy for the problem. In particular, the asymptotic elasticity of U plays a decisive role: existence can be shown when it is strictly greater at -∞ than at +∞.

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