Optimal Risk Sharing with Limited Liability

82 Pages Posted: 11 Feb 2012

See all articles by Semyon Malamud

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Huaxia Rui

University of Rochester - Simon Business School

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management

Date Written: February 1, 2012

Abstract

We solve the general problem of optimal risk sharing among a nite number of agents with limited liability. We show that the optimal allocation is characterized by endogenously determined ranks assigned to the participating agents and a hierarchical structure of risk sharing, where all agents take on risks only above the agent-speci fic thresholds determined by their ranks. When all agents have CARA utilities, linear risk sharing is optimal between two adjacent thresholds. We use our general characterization of optimal risk sharing with limited liability to solve the problem of optimal insurance design with multiple insurers. We show that the optimal thresholds, or deductibles, can be efficiently calculated through the fixed point of a contraction mapping. We then use this contraction mapping technique to derive a number of comparative statics results for optimal insurance design and its dependence on microeconomic characteristics.

Keywords: optimal risk sharing, limited liability, optimal insurance design

JEL Classification: A10, D86, G22

Suggested Citation

Malamud, Semyon and Rui, Huaxia and Whinston, Andrew B., Optimal Risk Sharing with Limited Liability (February 1, 2012). Swiss Finance Institute Research Paper No. 12-05, Available at SSRN: https://ssrn.com/abstract=2002844 or http://dx.doi.org/10.2139/ssrn.2002844

Semyon Malamud (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Huaxia Rui

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management ( email )

CBA 5.202
Austin, TX 78712
United States
512-471-8879 (Phone)

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