We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market consisting of one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either over the positive real line or over the whole real line, is bounded from above. We also find that , when wealth is required to satisfy the no-bankruptcy constraint, the boundedness assumption can be dropped provided that we impose a certain integrability condition , 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.
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 over the positive real line or over 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.
R
consisting of
with
R
also find that , when wealth is required to satisfy the no-bankruptcy constraint, the
further find that the
R
a certain integrability condition
suitable integrability conditions