Related papers: A risk model with an observer in a Markov environm…

In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [1] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In…

We used the random walk to model the problem of reserves. The classic case of a stochastic process is the example of random walks, which are used to study a set of phenomena and, particularly, as in this article, models of reserves…

In this paper a class of Ornstein--Uhlenbeck processes driven by compound Poisson processes is considered. The jumps arrive with exponential waiting times and are allowed to be two-sided. The jumps are assumed to form an iid sequence with…

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 consider a risk model where deficits after ruin are covered by a new type of reinsurance contract that provides capital injections. To allow the insurance company's survival after ruin, the reinsurer injects capital only at ruin times…

Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…

In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin.…

Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…

This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…

We propose a statistical model for networks of event count sequences built on a cascade structure. We assume that each event triggers successor events, whose counts follow additive probability distributions; the ensemble of counts is given…

It has been understood that the "local" existence of the Markowitz' optimal portfolio or the solution to the local-risk minimization problem is guaranteed by some specific mathematical structures on the underlying assets price processes…

We derive exact tail asymptotics of the Parisian ruin probability for Gaussian risk models driven by locally self-similar Gaussian processes with a power-type deterministic trend. The considered setting includes non-stationary Gaussian…

We consider a random walk with a negative drift and with a jump distribution which under Cram\'er's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably…

We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…

We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…

We consider the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite time horizon which is generated by a Partially Observable Markov Decision Process (POMDP). The certainty equivalent…

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…

We address the problem of reinforcement learning in which observations may exhibit an arbitrary form of stochastic dependence on past observations and actions, i.e. environments more general than (PO)MDPs. The task for an agent is to attain…

This paper studies the properties of the Multiply Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs…

Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…