Optimal reinsurance and dividend distribution policies in the cramér-lundberg model

We consider that the reserve of an insurance company follows a Cramér-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cum...

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Autores principales: Azcue, P., Muler, N.
Formato: JOUR
Materias:
Cramér-Lundberg process
Dividend payouts
Dynamic programming principle
Hamilton-Jacobi-Bellman equation
Insurance
Reinsurance
Risk control
Viscosity solution
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09601627_v15_n2_p261_Azcue
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_09601627_v15_n2_p261_Azcue2023-10-03T15:53:41Z Optimal reinsurance and dividend distribution policies in the cramér-lundberg model Azcue, P. Muler, N. Cramér-Lundberg process Dividend payouts Dynamic programming principle Hamilton-Jacobi-Bellman equation Insurance Reinsurance Risk control Viscosity solution We consider that the reserve of an insurance company follows a Cramér-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cumulative expected discounted dividend payouts. We study the usual cases of excess-of-loss and proportional reinsurance as well as the family of all possible reinsurance contracts. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal band strategy. We also describe the optimal value function for small initial reserves. © 2005 Blackwell Publishing Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09601627_v15_n2_p261_Azcue
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cramér-Lundberg process
Dividend payouts
Dynamic programming principle
Hamilton-Jacobi-Bellman equation
Insurance
Reinsurance
Risk control
Viscosity solution
spellingShingle Cramér-Lundberg process
Dividend payouts
Dynamic programming principle
Hamilton-Jacobi-Bellman equation
Insurance
Reinsurance
Risk control
Viscosity solution
Azcue, P.
Muler, N.
Optimal reinsurance and dividend distribution policies in the cramér-lundberg model
topic_facet Cramér-Lundberg process
Dividend payouts
Dynamic programming principle
Hamilton-Jacobi-Bellman equation
Insurance
Reinsurance
Risk control
Viscosity solution
description We consider that the reserve of an insurance company follows a Cramér-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cumulative expected discounted dividend payouts. We study the usual cases of excess-of-loss and proportional reinsurance as well as the family of all possible reinsurance contracts. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal band strategy. We also describe the optimal value function for small initial reserves. © 2005 Blackwell Publishing Inc.
format JOUR
author Azcue, P.
Muler, N.
author_facet Azcue, P.
Muler, N.
author_sort Azcue, P.
title Optimal reinsurance and dividend distribution policies in the cramér-lundberg model
title_short Optimal reinsurance and dividend distribution policies in the cramér-lundberg model
title_full Optimal reinsurance and dividend distribution policies in the cramér-lundberg model
title_fullStr Optimal reinsurance and dividend distribution policies in the cramér-lundberg model
title_full_unstemmed Optimal reinsurance and dividend distribution policies in the cramér-lundberg model
title_sort optimal reinsurance and dividend distribution policies in the cramér-lundberg model
url http://hdl.handle.net/20.500.12110/paper_09601627_v15_n2_p261_Azcue
work_keys_str_mv AT azcuep optimalreinsuranceanddividenddistributionpoliciesinthecramerlundbergmodel
AT mulern optimalreinsuranceanddividenddistributionpoliciesinthecramerlundbergmodel
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