Optimal Insurance Purchase Strategies via Optimal Multiple Stopping Times

26 Pages Posted: 7 Oct 2014 Last revised: 18 Feb 2015

See all articles by Rodrigo Targino

Rodrigo Targino

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Georgy Sofronov

Macquarie University - Department of Statistics

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Date Written: October 6, 2014

Abstract

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems of direct relevance to applications in insurance for Operational Risk. Within this context we study a class of insurance products where the policy holder has the option to insure k of its annual Operational Risk losses in a horizon of T years. This involves a choice of k out of T years in which to apply the insurance policy coverage by making claims against losses in the given year. The insurance product structure presented can accommodate any kind of annual mitigation, but we present two basic generic insurance policy structures that can be combined to create more complex types of coverage. Following the Loss Distributional Approach (LDA) with Poisson distributed annual loss frequencies and Inverse-Gaussian loss severities we are able to characterize in closed form analytical expressions for the multiple optimal decision strategy that minimizes the expected Operational Risk loss over the next T years. For the cases where the combination of insurance policies and LDA model does not lead to closed form expressions for the multiple optimal decision rules, we also develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.

Keywords: Multiple stopping rules, Operational risk, Insurance

JEL Classification: C61, G32, G22

Suggested Citation

Targino, Rodrigo and Peters, Gareth and Sofronov, Georgy and Shevchenko, Pavel V., Optimal Insurance Purchase Strategies via Optimal Multiple Stopping Times (October 6, 2014). Available at SSRN: https://ssrn.com/abstract=2505973 or http://dx.doi.org/10.2139/ssrn.2505973

Rodrigo Targino (Contact Author)

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics ( email )

Praia de Botafogo
Rio de Janeiro, 22250-900
Brazil

HOME PAGE: http://https://sites.google.com/site/rodrigodossantostargino/

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Georgy Sofronov

Macquarie University - Department of Statistics ( email )

North Ryde
Sydney, New South Wales 2109
Australia

Pavel V. Shevchenko

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://www.businessandeconomics.mq.edu.au/contact_the_faculty/all_fbe_staff/pavel_shevchenko

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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