How Much We Gain by Surplus-Dependent Premiums-Asymptotic Analysis of Ruin Probability

Wang, Jing, Palmowski, Zbigniew and Constantinescu, Corina ORCID: 0000-0002-5219-3022 (2021) How Much We Gain by Surplus-Dependent Premiums-Asymptotic Analysis of Ruin Probability RISKS, 9 (9). 157-. ISSN 2227-9091, 2227-9091

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Abstract

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 linearly 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.

Item Type:	Article
Uncontrolled Keywords:	ruin probability, premiums dependent on reserves, risk process, Erlang distribution
Depositing User:	Symplectic Admin
Date Deposited:	18 Jan 2021 09:20
Last Modified:	16 Jun 2026 09:14
DOI:	10.3390/risks9090157
Open Access URL:	https://doi.org/10.3390%2Frisks9090157
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3113954
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