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.

中文翻译：

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离散市场模型不确定性下的效用最大化

我们研究了在一个具有安全资产和有限风险资产的无摩擦离散时间市场中，面对模型不确定性的代理商最大化终端效用的问题。我们表明，如果在正实线上或在整个实线上定义的效用函数从上方界定，则存在最优投资策略。我们进一步发现，只要我们施加与某些加强形式的无套利有关的适当可积性条件，就可以放弃有界假设。这些结果是在模型不确定性的替代框架中获得的，在该框架中，股票价格的所有可能动态都由同一滤波后的概率空间上的一组随机过程表示，而不是由一系列概率测度表示。