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Publisher: Elsevier

Issued date: 2011-11

Citation: European Journal of Operational Research, 2011, v. 214, nº 3, pp. 796-804

ISSN: 0377-2217

DOI: 10.1016-j.ejor.2011.05.035

Sponsor: Research partially supported by -RD Sistemas SA- -Comunidad Autónoma de Madrid- Spain, Grant S2009-ESP – 1594, and -MEyC- Spain, Grant ECO2009 – 14,457 – C04

Publisher version: http:-dx.doi.org-10.1016-j.ejor.2011.05.035

Project: Comunidad de Madrid. S2009-ESP-1685-RIESGOSGobierno de España. ECO2009-14457-C04

Keywords: Optimal reinsurance , Risk measure , Sensitivity , Stable optimal retention , Stop-loss reinsurance

Abstract:The optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches considera coherent or expectation bounded risk measure and minimize the global risk of the ceding companyunder adequate constraints. However, there is no consensThe optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches considera coherent or expectation bounded risk measure and minimize the global risk of the ceding companyunder adequate constraints. However, there is no consensus about the risk measure that the insurer mustuse, 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 reinsurancewith respect to the risk measure that the insurer uses. We will demonstrate that there is a ‘‘stable optimalretention’’ that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for manyrisk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop-losscontract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numericalexample presented.+-





Autor: Balbás, Alejandro; Balbás, Beatriz; Heras, Antonio

Fuente: http://e-archivo.uc3m.es


Introducción



Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Economía de la Empresa DEE - Artículos de Revistas 2011-11 Stable solutions for optimal reinsurance problems involving risk measures Balbás, Alejandro Elsevier European Journal of Operational Research, 2011, v.
214, nº 3, pp.
796-804 http:--hdl.handle.net-10016-13079 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid European Journal of Operational Research 214 (2011) 796–804 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com-locate-ejor Innovative Applications of O.R. Stable solutions for optimal reinsurance problems involving risk measures Alejandro Balbás ⇑, Beatriz Balbás, Antonio Heras 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 a r t i c l e i n f o Article history: Received 3 May 2010 Accepted 19 May 2011 Available online 27 May 2011 Keywords: Optimal reinsurance Risk measure Sensitivity Stable optimal retention Stop-loss reinsurance a b s t r a c t 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, ...





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