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Theory and Decision

Erschienen in:

01.01.2015

Catastrophe insurance equilibrium with correlated claims

verfasst von: Radoslav S. Raykov

Erschienen in: Theory and Decision | Ausgabe 1/2015

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Abstract

Catastrophe insurance differs from regular insurance in that individual claims are correlated and insurers have to pay more clients at once, which creates a liquidity strain. In this paper, I show two related findings: first, that when customers know their claims are correlated, this correlation can cause positive-sloping demand at low prices, and second, that because of this, a catastrophe insurance market can fail. Market failure is a stable equilibrium, which provides a better understanding of the frequent failures in catastrophe insurance markets.

Vorheriger Artikel Properties based on relative contributions for cooperative games with transferable utilities

Nächster Artikel An axiomatization of Choquet expected utility with cominimum independence

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For details see “The Price of Sunshine,” The Economist, June 8, 2006, p. 76, and Born and Viscusi (2006).

For example, some analysts estimated the notional value of CDS in General Motors at 70 times the actual GM debt outstanding (Adamo 2009).

Sjostrom (2009), p. 947.

For example, FASB Statement No. 5, “Accounting for Contingencies,” as discussed in Jaffee and Russell (1997).

For example, less than 20 % of the catastrophe exposure above $ 8 billion was reinsured in 1994 (Froot 1999).

Fox News, July 11, 2006.

For example, the California Earthquake Authority’s legal mandate obliges it to price policies close to the expected actuarial loss. Its existence does not seem to have hindered competition or market entry in the California market, which had more than 150 private insurers operating in 2005.

One can obtain similar results by assuming instead that $\alpha (t) \equiv t$.

The evidence quoted in Sect. 2 suggests that cases of partial settlement are extremely rare. However, the results remain very similar if instead the company splits available funds equally among claimants.

“Katrina damage ruling bad news for homeowners,” The Houston Chronicle, August 15, 2006.

“Jury Picked to Hear Katrina Insurance Lawsuit,” The Washington Post, January 8, 2007.

This includes one lawsuit file by three thousand homeowners from Mississippi and a another one by Mississippi Attorney General Jim Hood (Fox News, July 11, 2006).

To be precise, arbitrary but non-degenerate: this requires each firm to has a positive market share $s_k>0$, otherwise the market could end up being a monopoly or an oligopoly.

National Flood Insurance Program.

Florida Residential Property and Casualty Joint Underwriting Association.

Because demand is continuous by Fact 4.

Before the advent of modern firefighting technology, fires caused correlated damage similar to catastrophes: for example, the Great fire of London (seventeenth-centuary) destroyed 13,200 houses, 87 churches, and many public buildings.

Whether the entire regulatory capital $R$ or only a portion $\alpha (R)$ is highly liquid is immaterial here, since one can always set $\alpha (R)=R$.

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Titel: Catastrophe insurance equilibrium with correlated claims
verfasst von: Radoslav S. Raykov
Publikationsdatum: 01.01.2015
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 1/2015
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-013-9403-2

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