Stable solutions for optimal reinsurance problems involving risk measures |
| |
Authors: | Alejandro Balbás Beatriz Balbás Antonio Heras |
| |
Institution: | University Carlos III of Madrid, CL. Madrid, 126, 28903 Getafe, Madrid, Spain University of Castilla la Mancha, Avda. Real Fábrica de Seda, s/n, 45600 Talavera, Toledo, Spain University Complutense of Madrid, Somosaguas-Campus, 28223 Pozuelo de Alarcón Madrid, Spain |
| |
Abstract: | The optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others.This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a “stable optimal retention” that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop-loss contract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numerical example presented. |
| |
Keywords: | Optimal reinsurance Risk measure Sensitivity Stable optimal retention Stop-loss reinsurance |
本文献已被 ScienceDirect 等数据库收录! |
|