文章基本信息

标题：How Much We Gain by Surplus-Dependent Premiums—Asymptotic Analysis of Ruin Probability
本地全文：下载
作者：Jing Wang ; Jing Wang ; Jing Wang 等
期刊名称：Risks
印刷版ISSN：2227-9091
出版年度：2021
卷号：9
期号：1
页码：157
DOI：10.3390/risks9090157
语种：English
出版社：MDPI, Open Access Journal
摘要：In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential claims scenario, Erlang (2) claim sizes. Applying the approximation theory of solutions of linear ordinary differential equations, we derive the asymptotics of the ruin probabilities when the initial reserve tends to infinity. When considering premiums that are <i>linearly</i> dependent on reserves, representing, for instance, returns on risk-free investments of the insurance capital, we firstly derive explicit solutions of the ordinary differential equations under considerations, in terms of special mathematical functions and integrals, from which we can further determine their asymptotics. This allows us to recover the ruin probabilities obtained for general premiums dependent on reserves. We compare them with the asymptotics of the equivalent ruin probabilities when the premium rate is fixed over time, to measure the gain generated by this additional mechanism of binding the premium rates with the amount of reserve owned by the insurance company.