On the evaluation of finite-time ruin probabilities in a dependent risk model

We consider an insurance risk model with extended flexibility, under which claims arrive according to a point process with an order statistics (OS) property, their amounts may have any joint distribution and the premium income is accumulated following any nondecreasing, possibly discontinuous real valued function. We generalize the definition of an OS point process, assuming it is generated by an arbitrary cdf allowing jump discontinuities, which corresponds to an arbitrary (possibly discontinuous) claim arrival cumulative intensity function. The latter feature is appealing for insurance applications since it allows to consider clusters of claims arriving instantaneously. Under these general assumptions, a closed form expression for the joint distribution of the time to ruin and the deficit at ruin is derived, which remarkably involves classical Appell polynomials. Corollaries of our main result generalize previous non-ruin formulas e.g., those obtained by Ignatov and Kaishev

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Ruin and Deficit Under Claim Arrivals with the Order Statistics Property

Dimitrova

Kaishev

Ignatov

2018

Methodol Comput Appl Probab

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Analysis of an aggregate loss model in a Markov renewal regime

Ramírez‐Cobo

Carrizosa

Lillo

2021

Applied Mathematics and Computation

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In this article we consider an aggregate loss model with dependent losses. The loss occurrence process is governed by a two-state Markovian arrival process ( MAP 2 ), a Markov renewal process that allows for (1) correlated inter-loss times, (2) non-exponentially distributed inter-loss times and, (3) overdisperse loss counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real OpRisk database, the aggregate loss model is estimated by fitting separately the inter-loss times and severities. The MAP 2 is estimated via direct maximization of the likelihood function, and severities are modeled by the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the fit provided by the Poisson process, the results point out that taking into account the dependence and overdispersion in the inter-loss times distribution leads to higher capital charges.

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On an insurance ruin model with a causal dependence structure and perturbation

Li,

Sendova,

Yang

2024

Journal of Computational and Applied Mathematics

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On the evaluation of finite-time ruin probabilities in a dependent risk model

Cited by 6 publications

References 23 publications

Ruin and Deficit Under Claim Arrivals with the Order Statistics Property

Ruin and Deficit Under Claim Arrivals with the Order Statistics Property

Analysis of an aggregate loss model in a Markov renewal regime

On an insurance ruin model with a causal dependence structure and perturbation

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