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The maximum surplus in a finite‐time interval for a discrete‐time risk model with exchangeable, dependent claim occurrences
Author(s) -
Gebizlioglu Omer L.,
Eryilmaz Serkan
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2415
Subject(s) - mathematics , interval (graph theory) , independent and identically distributed random variables , sequence (biology) , distribution (mathematics) , discrete time and continuous time , computation , risk model , aggregate (composite) , econometrics , statistics , mathematical optimization , random variable , combinatorics , mathematical analysis , algorithm , materials science , biology , composite material , genetics
This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed.