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INSURANCE LOSS COVERAGE UNDER RESTRICTED RISK CLASSIFICATION: THE CASE OF ISO-ELASTIC DEMAND

Published online by Cambridge University Press:  16 February 2016

MingJie Hao ,
Angus S. Macdonald ,
Pradip Tapadar  and
R. Guy Thomas
MingJie Hao
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK E-Mail: mh586@kent.ac.uk
Angus S. Macdonald
Affiliation:
Department of Actuarial Mathematics and Statistics, and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK E-Mail: A.S.Macdonald@hw.ac.uk
Pradip Tapadar*
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK
R. Guy Thomas
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK E-mail: R.G.Thomas@kent.ac.uk
*
E-Mail: P.Tapadar@kent.ac.uk
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Abstract

This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection (in the economist's sense); and “loss coverage”, defined as the expected population losses compensated by insurance. We consider both equal elasticities for high and low risk-groups, and then different elasticities. In the equal elasticities case, adverse selection is always higher under pooling than under risk-differentiated premiums, while loss coverage first increases and then decreases with demand elasticity. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore that if demand elasticity is sufficiently low, adverse selection is not always a bad thing.

Keywords

Adverse selectionloss coveragerisk classificationequilibrium premiumiso-elastic demand
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 2 , May 2016 , pp. 265 - 291
Copyright
Copyright © Astin Bulletin 2016 

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