TY - JOUR
T1 - Drawdown analysis for the renewal insurance risk process
AU - Landriault, David
AU - Li, Bin
AU - Li, Shu
N1 - Funding Information:
This work was supported by individual grants by the Natural Sciences and Engineering Research Council of Canada to David Landriault [grant number 341316] and Bin Li [grant number 05828]. Support from a start-up grant from the University of Waterloo is acknowledged by Bin Li, as is support from the Canada Research Chair program by David Landriault. Shu Li acknowledges the support from the James C. Hickman Scholar program of the Society of Actuaries, and from the Waterloo Research Institute in Insurance, Securities and Quantitative Finance.
Publisher Copyright:
© 2016 Taylor & Francis.
PY - 2017/3/16
Y1 - 2017/3/16
N2 - In this paper, we study some drawdown-related quantities in the context of the renewal insurance risk process with general interarrival times and phase-type distributed jump sizes. We make use of some recent results on the two-sided exit problem for the spectrally negative Markov additive process and a fluid flow analogy between certain queues and risk processes to solve for the two-sided exit problem of the renewal insurance risk process. The two-sided exit quantities are later shown to be central to the analysis of drawdown quantities including the drawdown time, the drawdown size, the running maximum (minimum) at the drawdown time, the last running maximum time prior to drawdown, the number of jumps before drawdown and the number of excursions from running maximum before drawdown. Finally, we consider another application of our methodology for the study of the expected discounted dividend payments until ruin.
AB - In this paper, we study some drawdown-related quantities in the context of the renewal insurance risk process with general interarrival times and phase-type distributed jump sizes. We make use of some recent results on the two-sided exit problem for the spectrally negative Markov additive process and a fluid flow analogy between certain queues and risk processes to solve for the two-sided exit problem of the renewal insurance risk process. The two-sided exit quantities are later shown to be central to the analysis of drawdown quantities including the drawdown time, the drawdown size, the running maximum (minimum) at the drawdown time, the last running maximum time prior to drawdown, the number of jumps before drawdown and the number of excursions from running maximum before drawdown. Finally, we consider another application of our methodology for the study of the expected discounted dividend payments until ruin.
KW - constant dividend barrier strategy
KW - drawdown
KW - fluid flow technique
KW - renewal insurance risk process
KW - ruin probability
KW - two-sided exit problem
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U2 - 10.1080/03461238.2015.1123174
DO - 10.1080/03461238.2015.1123174
M3 - Article
AN - SCOPUS:84954229065
SN - 0346-1238
VL - 2017
SP - 267
EP - 285
JO - Scandinavian Actuarial Journal
JF - Scandinavian Actuarial Journal
IS - 3
ER -