On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets

Rásonyi, Miklós and Meireles-Rodrigues, Andrea (2020) On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets. MATHEMATICAL FINANCE: AN INTERNATIONAL JOURNAL OF MATHEMATICS, STATISTICS AND FINANCIAL ECONOMICS, Accept. ISSN 0960-1627

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Abstract

We study the problem of maximising 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.

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