Separation Without Exclusion in Financial Insurance

• Author: James R. Thompson,Eric Stephens
• Published date: 01 December 2015
• Date: 01 December 2015
• DOI: http://doi.org/10.1111/jori.12038

©2014 The Journal of Risk and Insurance. Vol.82, No. 4, 853–864 (2015).

DOI: 10.1111/jori.12038

Separation Without Exclusion in Financial

Insurance

Eric Stephens

James R. Thompson

Abstract

This article develops a model of linearly priced financial insurance sold by

default-prone insurers. It shows that when insurers differ in their default

probabilities there can exist equilibria in which different risk types partially

or completely self-sort into insurance contracts offered by different insurers.

Partial separation can occur when insurer default and insurance risks are un-

correlated. Full separation is possible when they are correlated. For example,

low-risk insured parties may match with higher default-risk insurers, while

high-risk insured parties match with lower default-risk insurers.

Introduction

In their seminal articles, Rothschild and Stiglitz (1976) and Wilson (1977) develop a

framework in which insurers can screen buyers through a menu of contracts wherein

low-risk individuals purchase relatively cheaper insurance than high-risk individuals

in return for less coverage. Existence of this type of separating equilibrium depends,

crucially, on the assumption that contracts are exclusive. Without exclusivity, prices

are typically assumed to be linear, and separation of risk types through a market

mechanism cannot generally be achieved.

Wedevelop a model of a market for financial insurance that contains two nonstandard

assumptions: insurance providers may default on their obligations, and pricing of

contracts is linear. We show that privately known type information can be revealed

in equilibrium, despite linear pricing. Our insured party (buyer) can be “risky” or

“safe,” with the former more likely to experience a loss. The buyer chooses how much

to insure with a stable “good” insurer versus how much to insure with an unstable

Eric Stephens is at Carleton University. Stephens can be contacted via

e-mail: eric.stephens@carleton.ca. James R. Thompson is at the University of Waterloo.

Thompson can be contacted via e-mail: james@uwaterloo.ca. We are grateful to Mike Hoy,

Casey Rothschild, Stefano Giglio, Jano Zabojnik, three anonymous referees, the editor, and

seminar participants at the 2011 Risk Theory Society (Little Rock), 2011 WFA (Santa Fe),

2011 FIRS (Sydney), University of Alberta, University of Toronto, and 2010 CEA for helpful

comments. Note that part of this article was written while Thompson was visiting the Wharton

School, which he would like to thank for its hospitality.Financial support provided by SSHRC

Grant 435-2013-0180 is gratefully acknowledged.

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