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Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models

Riccardo Brignone, Ioannis Kyriakou and Gianluca Fusai

Insurance: Mathematics and Economics, 2021, vol. 96, issue C, 232-247

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 computation of 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 (search for similar items in EconPapers)
JEL-codes: C15 C63 G13 G22 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.insmatheco.2020.12.002

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