Analytical Approximation for Distorted Expectations

This paper provides an efficient and accurate approximation for the distorted expectation of a risk factor when its density function or characteristic function is given in an analytical form. The fast Fourier transform (FFT) algorithm is used to set up an approximation for the distorted density function with a truncated sum of its Fourier-cosine series expansion on a finite interval. The resulting truncation approximation leads to an analytical approximation for the distorted expectation. The proposed approach can be used in different branches of applications of distorted expectations, such as in risk management, portfolio optimization and conic finance