Quantifying Ruin Metrics in a Diffusion-Driven Erlang (2) Risk Model with Dependency Modeled using the Spearman Copula.

Abstract

This paper focuses on the perturbation of an Erlang (2) risk model by a diffusion process, challenging the assumption of independence between claim amounts and inter claim durations. To account for a tail dependency structure, we introduce the Spearman copula, enabling the evaluation of Gerber-Shiu functions and ruin probabilities associated with this model. Our analysis delves into the Laplace transforms of the discounted penalty function and the probability of ruin. Towards the conclusion, explicit expressions are derived, accompanied by numerical examples illustrating ruin probabilities for individual claim sizes with exponential distributions.