Related papers: A characterization of progressively equivalent pro…
In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity…
Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…
Dealing with compound renewal process with generally distributed jump sizes and inter-renewal intervals, we focus on the approximation for the fixed-probability level, which is the core of inverse level crossing problem. We are developing…
In this note we present studies of coverage and power for confidence intervals for a Poisson process with known background calculated using the Likelihood ratio (aka Feldman & Cousins) ordering with Bayesian treatment of uncertainties in…
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…
The compound decision problem for a vector of independent Poisson random variables with possibly different means has half a century old solution. However, it appears that the classical solution needs smoothing adjustment even when there are…
In this paper, we build on the techniques developed in Albrecher et al. (2013), to generate initial-boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive…
This article constructs a class of random probability measures based on exponentially and polynomially tilting operated on the laws of completely random measures. The class is proved to be conjugate in that it covers both prior and…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
Plant differently colored points in the plane, then let random points ("Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions…
We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all…
We prove existence and uniqueness of the invariant measure and exponential mixing in the total-variation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions…
We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and…
In this paper we study the problem of Multiplicative Poisson Equation (MPE) bounded solution existence in the generic discrete-time setting. Assuming mixing and boundedness of the risk-reward function, we investigate what conditions should…
We consider the Dirichlet problem for equation involving a general operator associated with a symmetric transient regular Dirichlet form and bounded Borel measure on the right-hand side of the equation. We introduce a new function space…
We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…
In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…