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Stable Risk Sharing and Its Monotonicity

39 Pages Posted: 16 Jun 2017  

Xin Chen

University of Illinois at Urbana-Champaign

Zhenyu Hu

National University of Singapore (NUS) - Department of Decision Sciences

Shuanglong Wang

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign

Date Written: June 15, 2017

Abstract

We consider a risk sharing problem in which agents pool their random costs together and seek an allocation rule to redistribute the risk back to each agent. The problem is put into a cooperative game framework and we focus on two salient properties of an allocation rule: stability and monotonicity employing concepts of core and population monotonicity from cooperative game theory. When the risks of the agents are measured by coherent risk measures, we construct a risk allocation rule based on duality theory and establish its stability. When restricting the risk measures to the class of distortion risk measures, the duality-based risk allocation rule is population monotonic if the random costs are independent and log-concave. For the case with dependent normally distributed random costs, a simple condition on the dependence structure is identified to ensure the monotonicity property.

Keywords: risk allocation, cooperative game, coherent risk measure, distortion risk measure

JEL Classification: C71, G22, G32

Suggested Citation

Chen, Xin and Hu, Zhenyu and Wang, Shuanglong, Stable Risk Sharing and Its Monotonicity (June 15, 2017). Available at SSRN: https://ssrn.com/abstract=2987631

Xin Chen

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Zhenyu Hu (Contact Author)

National University of Singapore (NUS) - Department of Decision Sciences ( email )

NUS Business School
BIZ 1 Building, #02-01, 1 Business Link
117592
Singapore

Shuanglong Wang

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

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