The paper studies the ruin probability for an insurer's surplus process when claim arrivals are governed by a Multiply Iterated Poisson Process (MIPP). This framework generalizes the classical Cram\'er-Lundberg model by permitting claims to arrive in clusters, which makes it well suited for representing catastrophic insurance events. The main result is the development of explicit conditions for ultimate ruin, demonstrating that the ruin probability is driven chiefly by the jump intensity and the number of iterations. In addition, we derive integro-differential equations for both survival and ruin probabilities and obtain their Laplace transforms. These transforms are connected through recursive relations that tie ruin probabilities at successive iteration levels. We further propose a Cram\'er-Lundberg-type approximation, yielding asymptotic formulas for ruin probabilities together with a Lundberg-style bound. Finally, numerical experiments - along with comparisons to the classical model - are included to support the theory and to illustrate how claim clustering affects an insurer's likelihood of ruin.
The paper studies finite-horizon ruin for an insurance company with several lines of business admitting heavy-tailed claims. The claim amount process of the insurance company is modeled as a multivariate increasing L\'evy process possibly perturbed with fluctuations. A relevant insolvency event may involve the failure...
This paper provides a complete analytical characterization of the joint distribution of state counts before run-based absorption in multistate discrete-time processes. For sequences of independent and identically distributed (i.i.d.) random variables, we derive the exact joint distribution, revealing an elegant geometr...
Fahreddin Kalkan, İsmail Kınacı, Coşkun Kuş· Hacettepe Journal of Mathema...· 0 citations
This study considers a dependent insurance risk model in which premium income is represented by a stochastic compound Poisson process and the claim mechanism incorporates dependence between claim amounts and subsequent inter-claim times through a stochastic threshold structure. The Gerber–Shiu expected discounted penal...
Chun-Yu Xue· Asian Journal of Probability...· 0 citations
The Gambler's Ruin problem is one of the classical stochastic models of an agent who gains or loses capital repeatedly, till reaching his target level or till his ruin. In this paper, the problem is theoretically analyzed and solved by Monte Carlo simulation. This paper obtains the closed-form expression for the ruin p...
Guangxiang Xu· Finance & Economics· 0 citations
We study dynamic physical hedging for insurers exposed jointly to catastrophe losses and stochastic reconstruction costs. Surplus evolves as a controlled jump diffusion whose loss amplitude combines marked catastrophe severity, an exogenous mean-reverting cost factor, and endogenous mitigation. We establish well-posedn...
Paramahansa Pramanik, Michael Bowdin· 0 citations
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