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Mean field and n ‐agent games for optimal investment under relative performance criteria
Author(s) -
Lacker Daniel,
Zariphopoulou Thaleia
Publication year - 2019
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12206
Subject(s) - constant (computer programming) , economics , portfolio , construct (python library) , asset (computer security) , microeconomics , investment (military) , class (philosophy) , population , project portfolio management , competition (biology) , econometrics , mathematical economics , financial economics , computer science , ecology , demography , computer security , management , artificial intelligence , sociology , politics , project management , political science , law , biology , programming language
We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log‐normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mean field games, which we show are unique in the class of constant equilibria. In the CARA case, competition drives agents to invest more in the risky asset than they would otherwise, while in the CRRA case competitive agents may over‐ or underinvest, depending on their levels of risk tolerance.