Premium
On utility maximization under model uncertainty in discrete‐time markets
Author(s) -
Rásonyi Miklós,
MeirelesRodrigues Andrea
Publication year - 2021
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.12284
Subject(s) - utility maximization , utility maximization problem , discrete time and continuous time , arbitrage , economics , expected utility hypothesis , bounded function , mathematical economics , real line , econometrics , maximization , isoelastic utility , stock (firearms) , incomplete markets , asset (computer security) , mathematical optimization , mathematics , computer science , microeconomics , financial economics , mechanical engineering , mathematical analysis , statistics , computer security , discrete mathematics , engineering
We study the problem of maximizing terminal utility for an agent facing model uncertainty, in a frictionless discrete‐time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either on the positive real line or on the whole real line, is bounded from above. We further find that the boundedness assumption can be dropped, provided that we impose suitable integrability conditions, related to some strengthened form of no‐arbitrage. These results are obtained in an alternative framework for model uncertainty, where all possible dynamics of the stock prices are represented by a collection of stochastic processes on the same filtered probability space, rather than by a family of probability measures.