2019/06/03 by Wenyuan Wang, Ping Chen, Wang, Wenyuan +3
Decision Sciences · Mathematics · Social Sciences · #60G51 #91B30 #97M30 #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1906.01449
openalex publication_date 2019/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers an insurance surplus process modeled by a spectrally negative Lévy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the joint distribution of the time of drawdown, the running maximum at drawdown, the last minimum before drawdown, the surplus before drawdown and the surplus at drawdown (may not be deficit in this case), which generalizes the known results on the classical expected discounted penalty function in Gerber and Shiu (1998). The results have semi-explicit expressions in terms of the q-scale functions and the Lévy measure associated with the Lévy process. As applications, the obtained result is applied to recover results in the literature and to obtain new results for the Gerber-Shiu function at ruin for risk processes embedded with a loss-carry-forward taxation system or a barrier dividend strategy. Moreover, numerical examples are provided to illustrate the results.