Data from Wroclaw University of Science and Technology Broaden Understanding of Risk Management (Diffusion Approximations of the Ruin Probability for the Insurer-Reinsurer Model Driven by a Renewal Process): Insurance – Risk Management

2022 JUL 11 (NewsRx) -- By a News Reporter-Staff News Editor at Insurance Daily News -- Current study results on risk management have been published. According to news reporting from Wroclaw, Poland, by NewsRx journalists, research stated, “We introduce here a diffusion-type approximation of the ruin probability both in finite and infinite time for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. This type of process is often called the insurer-reinsurer model.”

Our news correspondents obtained a quote from the research from Wroclaw University of Science and Technology: “We assume that the flow of claims is governed by a general renewal process. A simple ruin probability formula for the model is known only in infinite time for the special case of the Poisson process and exponentially distributed claims. Therefore, there is a need for simple analytical approximations. In the literature, in the infinite-time case, for the Poisson process, a De Vylder-type approximation has already been introduced. The idea of the diffusion approximation presented here is based on the weak convergence of stochastic processes, which enables one to replace the original risk process with a Brownian motion with drift. By applying this idea to the insurer-reinsurer model, we obtain simple ruin probability approximations for both finite and infinite time.”

According to the news reporters, the research concluded: “We check the usefulness of the approximations by studying several claim amount distributions and comparing the results with the De Vylder-type approximation and Monte Carlo simulations. All the results show that the proposed approximations are promising and often yield small relative errors.”

For more information on this research see: Diffusion Approximations of the Ruin Probability for the Insurer-Reinsurer Model Driven by a Renewal Process. Risks, 2022,10(129):129. (Risks - http://www.mdpi.com/journal/risks). The publisher for Risks is MDPI AG.

A free version of this journal article is available at https://doi.org/10.3390/risks10060129.

Our news editors report that more information may be obtained by contacting Krzysztof Burnecki, Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland. Additional authors for this research include Marek A. Teuerle, Aleksandra Wilkowska.

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