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

Jing Wang, Zbigniew Palmowski and Corina Constantinescu
Additional contact information
Jing Wang: Department of Mathematical Sciences, Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, UK
Zbigniew Palmowski: Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
Corina Constantinescu: Department of Mathematical Sciences, Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, UK

Risks, 2021, vol. 9, issue 9, 1-17

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.

Keywords: ruin probability; premiums dependent on reserves; risk process; Erlang distribution (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-9091/9/9/157/pdf (application/pdf)
https://www.mdpi.com/2227-9091/9/9/157/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:9:y:2021:i:9:p:157-:d:622795

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().