Efficient optimisation for portfolio selections under prospect theory

Abstract

The prospect theory (PT) is one of the most useful tools for portfolio optimisation. The main concept of PT is to use a S-shaped value function to depict how human beings' mental behaviour affect their investment decisions under different risk levels. However, the complexity in the theory results in the difficulty in the proposal of efficient algorithms for global optimisation. In order to make improvements, we first approximate the S-shaped value function in PT with a piecewise linear (PWL) surrogate model, and equivalently transform the resulted problem into a continuous concave piecewise linear maximisation problem. Despite of the non-smoothness and non-convexity of the problem, we propose two local search algorithms based on the interior point method, and present the theoretical analysis on the convergence. Moreover, we propose a global search algorithm based on the proposed local search algorithms and the γ valid cut method in concave optimisation. The numerical experiments on the historical data of different assets obtained from Yahoo concern the comparisons of the proposed algorithms and the existing methods in the literature. The results confirm the performances of the proposed algorithm on efficiency and accuracy.