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

35 Pages Posted: 28 Jan 2021 Last revised: 26 Jul 2021

See all articles by Riccardo Brignone

Riccardo Brignone

University of Freiburg

Ioannis Kyriakou

Bayes Business School (formerly Cass), City, University of London

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa; Bayes Business School - City, University of London

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

Suggested Citation

Brignone, Riccardo and Kyriakou, Ioannis and Fusai, Gianluca, Moment-Matching Approximations for Stochastic Sums in Non-Gaussian Ornstein–Uhlenbeck Models. Insurance: Mathematics and Economics, 2021, 96, 232-247, Available at SSRN: https://ssrn.com/abstract=3744041

Riccardo Brignone

University of Freiburg ( email )

Freiburg, DE
Germany

Ioannis Kyriakou (Contact Author)

Bayes Business School (formerly Cass), City, University of London ( email )

Faculty of Actuarial Science & Insurance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom
+44 (0)20 7040 8738 (Phone)
+44 (0)20 7040 8881 (Fax)

HOME PAGE: http://www.bayes.city.ac.uk/experts/I.Kyriakou

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone, 18
Novara, 28100
Italy

HOME PAGE: http://https://upobook.uniupo.it/gianluca.fusai

Bayes Business School - City, University of London ( email )

106 Bunhill Row
London, EC2Y 8HB
Great Britain

HOME PAGE: http:// www.cass.city.ac.uk/experts/G.Fusai

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