1,720,996 research outputs found
Lundberg parameters for non standard risk processes
No full textWe consider risk processes with delayed claims in a Markovian environment, and we study the asymptotic behaviour of finite and infinite horizon ruin probabilities under the small claim assumption. We also consider multivariate risk processes of the same kind, and we give upper and lower bounds for the Lundberg parameters of the corresponding total reserve. Our results have strong analogies with those one in the paper by Juri (Super modular order and Lundberg exponents, 2002)
Large deviations for fractional Poisson processes
Full text linkWe prove large deviation principles for two versions of fractional Poisson processes: the main version is a renewal process, the alternative version is a weighted Poisson process. We also present asymptotic results for the ruin probabilities of an insurance model with a fractional Poisson claim number process. (C) 2013 Elsevier B.V. All rights reserved
Large deviation principles for telegraph processes
No full textThe aim of this paper is to present large deviation results for some telegraph random motions. We are not aware of any other results of this kind except the ones for the classical telegraph process (with drift). We start with the large deviation principle of the conditional laws given the number of changes of direction for the classical case; moreover, we compare the rate function with the one obtained for the non-conditional distributions. Finally, we study an inhomogeneous model and a planar telegraph motion. (C) 2012 Elsevier B.V. All rights reserved
FRACTIONAL DISCRETE PROCESSES: COMPOUND AND MIXED POISSON REPRESENTATIONS
No full textWe consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the Polya-Aeppli process, the Poisson inverse Gaussian process, and the negative binomial process. We also define and study some more general fractional versions with two fractional parameters
Large deviations for risk processes with reinsurance
Full text linkWe consider risk processes with reinsurance. A general family of reinsurance contracts is allowed, including proportional and excess-of-loss policies. Claim occurrence is regulated by a classical compound Poisson process or by a Markov-modulated compound Poisson process. We provide some large deviation results concerning these two risk processes in the small-claim case. Finally, we derive the so-called Lundberg estimate for the ruin probabilities and present a numerical example
Bayes factor for non-dominated statistical models
No full textThis paper deals with the definition of the Bayes factor (BF) for non-dominated statistical models, where the ordinary likelihood function is not defined. A general definition of BF is proposed, which also covers dominated models; its main properties are examined and its practical use discussed through some simple examples, aimed at illustrating the behaviour of the BF in non-standard problems. © 2001 Elsevier Science B.V
Alternative Forms of Compound Fractional Poisson Processes
Full text linkWe study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves. The corresponding distributions are obtained explicitly and proved to be solution of fractional equations of order less than one. Only in the final case treated in this paper, where the number of jumps is given by the fractional-difference Poisson process defined in Orsingher and Polito (2012), we have a fractional driving equation, with respect to the time argument, with order greater than one. Moreover, in this case, the compound Poisson process is Markovian and this is also true for the corresponding limiting process. All the processes considered here are proved to be compositions of continuous time random walks with stable processes (or inverse stable subordinators). These subordinating relationships hold, not only in the limit, but also in the finite domain. In some cases the densities satisfy master equations which are the fractional analogues of the well-known Kolmogorov one
Large deviation results on some estimators for stationary Gaussian processes
No full textIn this paper, we present large deviation results for estimators of some unknown parameters concerning
stationary Gaussian processes. We deal with both maximum likelihood estimators and posterior distributions;
moreover, we illustrate the differences between short-range- and long-range-dependent processes. As
a typical feature the rate functions for maximum likelihood estimators and posterior distributions are given
in terms of the same relative entropy and the roles of the two probability measures in the relative entropy
are exchanged. We define a sort of relative entropy with respect to the sampling process which in the i.i.d.
case corresponds to the relative entropy with respect to the common law of each single sample. In view
of potential applications in risk theory we prove large deviation results for estimators of the logarithmic
asymptotic decay rate of the tail of the supremum of a random walk with stationary Gaussian increments.
Finally, we present results for compound renewal processes with stationary Gaussian distributed rewards,
independent of i.i.d.Weibull distributed renewal times
On the asymptotic behavior of the hyperbolic Brownian motion
No full textThe main results in this paper concern large and moderate deviations for the radial component of a n-dimensional hyperbolic Brownian motion (for n≥2) on the Poincaré half-space. We also investigate the asymptotic behavior of the hitting probability Pη(T(n)η1<∞) of a ball of radius η1, as the distance η of the starting point of the hyperbolic Brownian motion goes to infinity
- …
