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On a risk model with claim investigation. (English) Zbl 1348.91151
Summary: 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. G. C. Taylor [“Probability of ruin under inflationary conditions or under experience rating”, Astin Bull. 10, No. 2, 149–162 (1979)], J. Cai and D. C. M. Dickson [Insur. Math. Econ. 30, No. 3, 389–404 (2002; Zbl 1074.91027)], and J. Trufin et al. [Appl. Stoch. Models Bus. Ind. 27, No. 6, 619–632 (2011; Zbl 1275.91079)]. 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.

MSC:
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
60K25 Queueing theory (aspects of probability theory)
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