Optimal Dynamic Reinsurance Policies Under Mean – CVaR – A Generalized Denneberg’s Absolute Deviation Principle

31 Pages Posted: 14 Mar 2018

See all articles by Ken Seng Tan

Ken Seng Tan

University of Waterloo

Pengyu Wei

University of Waterloo - Department of Statistics and Actuarial Science; University of New South Wales (UNSW) - ARC Centre of Excellence in Population Ageing Research (CEPAR); University of Oxford - Oxford-Man Institute of Quantitative Finance

Wei Wei

University of Waterloo - Department of Statistics and Actuarial Science

Sheng Chao Zhuang

University of Nebraska Lincoln

Date Written: January 28, 2018

Abstract

This paper studies the optimal dynamic reinsurance policy for an insurance company whose surplus is modeled by the diffusion approximation of the classical Cramér-Lundberg model. We assume the reinsurance premium is calculated according to a proposed Mean-CVaR premium principle which generalizes Denneberg's absolute deviation principle and expected value principle. Moreover, we require that both ceded loss and retention functions are non-decreasing to rule out moral hazard. Under the objective of minimizing the ruin probability, we obtain the optimal reinsurance policy explicitly and we denote the resulting treaty as the dual excess-of-loss reinsurance. This form of optimal treaty is new to the literature. It also demonstrates that reinsurance treaties such as the proportional and the standard excess-of-loss, which are typically found to be optimal in the dynamic reinsurance model, need not be optimal when we consider a more general optimization model.

Keywords: Dynamical Reinsurance, Mean-CVaR Premium Principle, Denneberg’s Absolute Deviation Principle, Ruin Probability

JEL Classification: C61 G22

Suggested Citation

Tan, Ken Seng and Wei, Pengyu and Wei, Wei and Zhuang, Sheng Chao, Optimal Dynamic Reinsurance Policies Under Mean – CVaR – A Generalized Denneberg’s Absolute Deviation Principle (January 28, 2018). Available at SSRN: https://ssrn.com/abstract=3138804 or http://dx.doi.org/10.2139/ssrn.3138804

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Pengyu Wei (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada

University of New South Wales (UNSW) - ARC Centre of Excellence in Population Ageing Research (CEPAR) ( email )

Level 6, Central Lobby (enter via East Lobby)
Australian School of Business Building
Sydney, New South Wales NSW 2052
Australia

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford, Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

Wei Wei

University of Waterloo - Department of Statistics and Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Croatia

Sheng Chao Zhuang

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

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