Showing 1 - 10 of 23
Persistent link: https://www.econbiz.de/10005380602
We discuss how to prove exponential upper bounds for simple fluid models driven by a finite state CTMC. In particular, we consider the fluid model of Anick, Mitra and Sondhi, in which the fluid is generated by N independent 0-1 Markovian sources. We also give a result on a generalized...
Persistent link: https://www.econbiz.de/10005254162
Consider a population in which the birth times are a Poisson process with rate [gamma] lifetimes are independent and identically distributed and lifetimes are independent of the birth process. In the paper we provide methods for calculation of several quantities involving the oldest member...
Persistent link: https://www.econbiz.de/10008874003
In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most...
Persistent link: https://www.econbiz.de/10010338093
Persistent link: https://www.econbiz.de/10013440228
Persistent link: https://www.econbiz.de/10011036210
Consider the American put and Russian option (Ann. Appl. Probab. 3 (1993) 603; Theory Probab. Appl. 39 (1994) 103; Ann. Appl. Probab. 3 (1993) 641) with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with...
Persistent link: https://www.econbiz.de/10008874892
Consider a random walk or Lévy process {St} and let [tau](u) = inf {t[greater-or-equal, slanted]0 : St u}, P(u)(·) = P(· [tau](u) < [infinity]). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time [tau](u) is described as u --> [infinity]. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for...</[infinity]).>
Persistent link: https://www.econbiz.de/10008874973
We study the tail asymptotics of the r.v. X(T) where {X(t)} is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail...
Persistent link: https://www.econbiz.de/10008875713
For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution [pi] of the maximum has a tail [pi](x,[infinity]) which is asymptotically proportional to . We supplement here this by a local result...
Persistent link: https://www.econbiz.de/10005074680