We consider a discrete-time stock market where agents' preferences are described by utility functions (defined on the real line) and they seek to optimise the expected utility of their terminal portfolio value.
This problem has been extensively treated in the case where the utility function is concave. Concavity corresponds to an assumed risk-averse attitude of agents. It may be argued that, in certain cases, agents are actually risk-seeking or at least their risk aversion is different on different intervals. Hence one should deal with the maximisation of a possibly non-concave utility function.
We present a fairly general existence result in a non-concave setting.
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