On a risk model with claim investigation

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• 作者：Mirabelle Huynh^a ; ^{m3huynh@uwaterloo.ca" class="auth_mail" title="E-mail the corresponding author} ; David Landriault^a ; Tianxiang Shi^b ; Gordon E. Willmot^a
• 关键词：Claim investigation ; Queueing system ; Gerber&ndash ; Shiu analysis ; Defective renewal equation ; Queueing theory ; Risk theory
• 刊名：Insurance: Mathematics and Economics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：65
• 期：Complete
• 页码：37-45
• 全文大小：485 K

文摘

In this paper, a queue-based claims investigation mechanism is considered to model an insurer’s claim processing practices. The resulting risk model may be viewed as a first step in developing models with more realistic claim investigation mechanisms. Related to claim investigations, claim settlement delays and time dependent payments have been studied in a ruin context by, e.g. Taylor (1979), Cai and Dickson (2002), and Trufin et al. (2011). However, little has been done on queue-based investigation mechanisms. We first demonstrate the impact of a particular claim investigation system on some common ruin-related quantities when claims arrive according to a compound Poisson process, and investigation times are of a combination of exponential form. Probabilistic interpretations for the defective renewal equation components are also provided. Finally, via numerical examples, we explore various risk management questions related to this problem such as how claim investigation strategies can help an insurer control its activities within its risk appetite.