Loss aversion, large deviation preferences and optimal portfolio weights for some classes of return processes

We propose a model of a loss averse investor who aims to maximize his expected wealth under certain constraints. The constraints are that he avoids, with high probability, incurring an (suitably defined) unacceptable loss. The methodology employed comes from the theory of large deviations. We explore a number of fundamental properties of the model and illustrate its desirable features. We demonstrate its utility by analyzing assets that follow some commonly used financial return processes: Fractional Brownian Motion, Jump Diffusion, Variance Gamma and Truncated Lévy.