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

35 Pages Posted: 28 Jan 2021

See all articles by Riccardo Brignone

Riccardo Brignone

University of Freiburg

Ioannis Kyriakou

City University London - Sir John Cass Business School

Gianluca Fusai

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

Date Written: December 7, 2020

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 (December 7, 2020). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3744041

Riccardo Brignone

University of Freiburg ( email )

Platz der Alten Synagoge, KG II
Platz der Alten Synagoge, KG II
Freiburg, DE
Germany

Ioannis Kyriakou (Contact Author)

City University London - Sir John Cass Business School ( 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.cass.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

Sir John Cass 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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