2025/05/16 by Michel Mandjes, Mandjes, Michel, Daniël Rutgers +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2505.11127
openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates an insurance model with a finite number of major clients and a large number of small clients, where the dynamics of the latter group are modeled by a spectrally positive Lévy process. We begin by analyzing this general model, in which the inter-arrival times are exponentially distributed (though not identically), and derive the closed-form Laplace transform of the ruin probability. Next, we examine a simplified version of the model involving only the major clients, and explore the tail asymptotics of the ruin probability, focusing on the cases where the claim sizes follow phase-type or regularly varying distributions. Finally, we derive the distribution of the overshoot over an exponentially distributed initial reserve, expressed in terms of its Laplace-Stieltjes transform.