Pareto-optimal reinsurance policies in the presence of individual risk constraints

Ambrose Lo () and Zhaofeng Tang ()
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Ambrose Lo: The University of Iowa
Zhaofeng Tang: The University of Iowa

Annals of Operations Research, 2019, vol. 274, issue 1, No 19, 395-423

Abstract: Abstract The notion of Pareto optimality is commonly employed to formulate decisions that reconcile the conflicting interests of multiple agents with possibly different risk preferences. In the context of a one-period reinsurance market comprising an insurer and a reinsurer, both of which perceive risk via distortion risk measures, also known as dual utilities, this article characterizes the set of Pareto-optimal reinsurance policies analytically and visualizes the insurer–reinsurer trade-off structure geometrically. The search of these policies is tackled by translating it mathematically into a functional minimization problem involving a weighted average of the insurer’s risk and the reinsurer’s risk. The resulting solutions not only cast light on the structure of the Pareto-optimal contracts, but also allow us to portray the resulting insurer–reinsurer Pareto frontier graphically. In addition to providing a pictorial manifestation of the compromise reached between the insurer and reinsurer, an enormous merit of developing the Pareto frontier is the considerable ease with which Pareto-optimal reinsurance policies can be constructed even in the presence of the insurer’s and reinsurer’s individual risk constraints. A strikingly simple graphical search of these constrained policies is performed in the special cases of Value-at-Risk and Tail Value-at-Risk.

Keywords: Distortion; 1-Lipschitz; Value-at-Risk; Pareto frontier; Multi-criteria optimization; Risk sharing (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10479-018-2820-4

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