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To accurately quantify landslide hazard in a region of Turkey, we develop new marked point process models within a Bayesian hierarchical framework for the joint prediction of landslide counts and sizes. To accommodate for the dominant role…
We review Markov models of surplus in life insurance based on a counting process following Norberg (1991), uniting probabilistic theory with elements of practice largely drawn from UK experience. First, we organize models systematically…
Folklore often treats the Markov Modulated Poisson Process as bursty because the variance divided by the expectation of counts is greater than unity. When viewed through the lens of the inter-event process, this ideally corresponds to a…
We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type…
Let (X_n,Y_n), n\ge 1 be bivariate random claim sizes with common distribution function F and let N(t), t \ge 0 be a stochastic process which counts the number of claims that occur in the time interval [0,t], t\ge 0. In this paper we derive…
In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
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…
The potential for cascading failure in power systems adds substantially to overall reliability risk. Monte Carlo sampling can be used with a power system model to estimate this impact, but doing so is computationally expensive. This paper…
The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information.…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\'olya-Aeppli process. It is shown that these processes…
We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the…
In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general…
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance…
The EU Solvency II directive recommends insurance companies to pay more attention to the risk management methods. The sense of risk management is the ability to quantify risk and apply methods that reduce uncertainty. In life insurance, the…