Portfolio optimization under safety first expected utility with nonlinear probability distortion. (June 2021) - Li, Yan; Mi, Hui
Highlights: Firstly, we study a portfolio selection problem under safety first expected utility model with distortion (SFEUD model) where the underlying probability scale is transformed by a nonlinear distortion function. Secondly, the general form of optimal solution to the problem is obtained, and the necessary and sufficient condition for existing such an optimal solution is also proved. Thirdly, an analytical solution to the optimal strategies under four different monotonic cases is further demonstrated. Abstract: In this paper, we study a portfolio selection problem under safety first expected utility model with distortion (SFEUD model) where the underlying probability scale is transformed by a nonlinear distortion function. By employing the quantile formulation and the relaxation method, we obtain the general form of optimal solution to the problem, and the necessary and sufficient condition for existing such an optimal solution is also proved. We further demonstrate an analytical solution to the optimal strategies under four different monotonic cases. What's more, the optimal terminal wealth process is replicated into a portfolio of options and deposits under specific circumstances. In addition, we empirically verify the model implication and figure out that investors' realization of disaster risk can explain the price change of call options to some degree.