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Risks 2017, 5(3), 51; doi:10.3390/risks5030051

An Integrated Approach to Pricing Catastrophe Reinsurance

1
Department of Finance, California State University, Fullerton, CA 92831, USA
2
Department of Finance & Law, California State University, Los Angeles, CA 90032, USA
*
Author to whom correspondence should be addressed.
Received: 3 July 2017 / Revised: 10 September 2017 / Accepted: 14 September 2017 / Published: 19 September 2017
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Abstract

We propose an integrated approach straddling the actuarial science and the mathematical finance approaches to pricing a default-risky catastrophe reinsurance contract. We first apply an incomplete-market version of the no-arbitrage martingale pricing paradigm to price the reinsurance contract as a martingale by a measure change, then we apply risk loading to price in—as in the traditional actuarial practice—market imperfections, the underwriting cycle, and other idiosyncratic factors identified in the practice and empirical literatures. This integrated approach is theoretically appealing for its merit of factoring risk premiums into the probability measure, and yet practical for being applicable to price a contract not traded on financial markets. We numerically study the catastrophe pricing effects and find that the reinsurance contract is more valuable when the catastrophe is more severe and the reinsurer’s default risk is lower because of a stronger balance sheet. We also find that the price is more sensitive to the severity of catastrophes than to the arrival frequency; implying (re)insurers should focus more on hedging the severity than the arrival frequency in their risk management programs. View Full-Text
Keywords: mathematical finance; actuarial science; catastrophe arrivals; catastrophe reinsurance; default risk; Monte Carlo simulation mathematical finance; actuarial science; catastrophe arrivals; catastrophe reinsurance; default risk; Monte Carlo simulation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chang, C.W.; Chang, J.S.K. An Integrated Approach to Pricing Catastrophe Reinsurance. Risks 2017, 5, 51.

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