Nash equilibria for relative investors via no-arbitrage arguments

Nicole Bäuerle () and Tamara Göll ()
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Nicole Bäuerle: Karlsruhe Institute of Technology (KIT)
Tamara Göll: Karlsruhe Institute of Technology (KIT)

Mathematical Methods of Operations Research, 2023, vol. 97, issue 1, No 1, 23 pages

Abstract: Abstract Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for n agents who try to maximize the expected utility of their relative wealth. The utility function can be rather general here. Exploiting the linearity of the stochastic integral and making use of the classical pricing theory we are able to express all Nash equilibrium investment strategies in terms of the optimal strategies for the classical one agent expected utility problems. The corresponding mean field problem is solved in the same way. We give four applications of specific financial markets and compare our results with those given in the literature.

Keywords: Portfolio optimization; Semimartingale market; Nash equilibrium; Relative investor; 91A35; 91A16; 91G20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-022-00804-x

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