Marginal Indemnification Function Formulation for Optimal Reinsurance

28 Pages Posted: 6 Feb 2017

See all articles by Sheng Chao Zhuang

Sheng Chao Zhuang

University of Nebraska Lincoln

Chengguo Weng

University of Waterloo

Ken Seng Tan

University of Waterloo

Hirbod Assa

University of Liverpool

Date Written: January 1, 2017

Abstract

In this paper, we propose to combine the Marginal Indemnification Function (MIF) formulation and the Lagrangian dual method to solve optimal reinsurance model with distortion risk measure and distortion reinsurance premium principle. The MIF method exploits the absolute continuity of admissible indemnification functions and formulates optimal reinsurance model into a functional linear programming of determining an optimal measurable function valued over a bounded interval. The MIF method was recently introduced to analyze the reinsurance model but without premium budget constraint. In this paper, a Lagrangian dual method is applied to combine with MIF to solve for optimal reinsurance solutions under premium budget constraint. Compared with the existing literature, the proposed integrated MIF-based Lagrangian dual method provides a more technically convenient and transparent solution to the optimal reinsurance design. To demonstrate the practicality of the proposed method, analytical solution is derived on a particular reinsurance model that involves minimizing Conditional Value at Risk (a special case of distortion function) and with the reinsurance premium being determined by the inverse-S shaped distortion principle.

Keywords: optimal reinsurance, marginal indemnification function, Lagrangian dual method, distortion risk measure, inverse-S shaped distortion premium principle

Suggested Citation

Zhuang, Sheng Chao and Weng, Chengguo and Tan, Ken Seng and Assa, Hirbod, Marginal Indemnification Function Formulation for Optimal Reinsurance (January 1, 2017). Insurance: Mathematics and Economics, Vol. 67, 2016. Available at SSRN: https://ssrn.com/abstract=2912007

Sheng Chao Zhuang

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

Chengguo Weng (Contact Author)

University of Waterloo ( email )

M3-200 Univ Ave W
Waterloo, Ontario N2L3G1
Canada
(1)888-4567 ext.31132 (Phone)

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Hirbod Assa

University of Liverpool ( email )

Institute for Financial and Actuarial Mathematics,
Liverpool, L18 8BF
United Kingdom
447522173132 (Phone)

HOME PAGE: http://sites.google.com/site/assahirbod/

Register to save articles to
your library

Register

Paper statistics

Downloads
16
Abstract Views
172
PlumX Metrics