Moment-Matching Approximations for Stochastic Sums in Non-Gaussian Ornstein–Uhlenbeck Models

Abstract

In this paper, we recall actuarial and financial applications of sums of dependent random variables that follow a non-Gaussian mean-reverting process and contemplate distribution approximations. Our work complements previous related studies restricted to lognormal random variables; we revisit previous approximations and suggest new ones. We then derive moment-based distribution approximations for random sums attuned to Asian option pricing and computationof risk measures of random annuities. Various numerical experiments highlight the speed-accuracy benefits of the proposed methods.

Keywords: Mean reversion, non-Gaussian processes, moment-matching, Asian option valuation, stochastic annuities

JEL Classification: G13, C63, C15, G22