Optimal reinsurance strategy under fixed cost and delay
type: Item
instance of: scholarly article
title: Optimal reinsurance strategy under fixed cost and delay
zbMATH Open document ID: 1172.62035
author: Masahiko Egami
author: Virginia R. Young
published in: Stochastic Processes and their Applications
publication date: 2009-04-02T00:00:00Z
review text: An optimal reinsurance strategy is considered where the insurance company (1) monitors the dynamics of its surplus process, (2) optimally chooses a time to begin negotiating with a reinsurer to buy quota-share, or proportional, reinsurance, which introduces an implementation delay (denoted by \(\Delta \geq 0\)), (3) chooses the optimal proportion at the beginning of the negotiation period, and (4) pays a fixed transaction cost when the contract is signed (\(\Delta \) units of time after negotiation begins). This setup leads to a combined problem of optimal stopping and stochastic control. A solution is obtained for the value function and the corresponding optimal strategy, while demonstrating the solution procedure in detail. It turns out that the optimal continuation region is a union of two intervals, a rather rare occurrence in optimal stopping. Numerical examples are given to illustrate the results and relevant economic insights from this model are discussed.
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 5539237
zbMATH Keywords: optimal stopping
zbMATH Keywords: implementation delay
zbMATH Keywords: transaction cost
reviewed by: Pavel Gapeev
MaRDI profile type: Publication
full work available at URL: j.spa.2008.04.005
OpenAlex ID: W2087253685
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DOI: 10.1016/J.SPA.2008.04.005
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description: scientific article; zbMATH DE number 5539237