Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/308611 
Year of Publication: 
2022
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 97 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 1-23
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Portfolio optimization
Semimartingale market
Nash equilibrium
Relative investor
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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