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We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the…

We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…

The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and…

This paper studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is…

We introduce the hybrid risk process, constructed via a time-change transformation applied to the solution of a hybrid stochastic differential equation. The framework covers several modern ruin settings, incorporating features like…

We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the…

Following an article by Muller and Pflug, we study the adjustment coefficient of ruin theory in a context of temporal dependency. We provide a consistent estimator of this coefficient, and perform some simulations.

The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.

This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently…

We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative…

We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…

In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider few versions of the ruin…

We study the asymptotic behavior of ruin probabilities, as the initial reserve goes to infinity, for a reserve process model where claims arrive according to a renewal process, while between the claim times the process has the dynamics of…

We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…

We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…

There is a lot of research on probabilistic transition systems. There are not many studies in probabilistic process models. The lack of investigation into the interactive aspect of probabilistic processes is mainly due to the difficulty…

The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some of the claim sizes. It is shown that this model can be considered as a particular case of the classical compound…

In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…

This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…