We investigate a shot noise process with subexponential shot marks occurring at renewal epochs. Our main result is a precise asymptotic formula for its tail probability. In doing so, some recent results regarding sums of randomly weighted subexponential random variables play a crucial role.

In the past two decades increasing computational power resulted in the development of more advanced claims reserving techniques, allowing the stochastic branch to overcome the deterministic methods, resulting in forecasts of enhanced quality. Hence, not only point estimates, but predictive...

A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the...

Determining distributions of the functions of random variables is a very important problem with a wide range of applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y=X1X2...

We propose two novel axioms for qualitative probability spaces (Bernstein, 1917; de Finetti, 1937; Koopman, 1940; Savage, 1954): (i) unlikely atoms, which requires that there is an event containing no atoms that is at least as likely as its complement; and (ii) third-order atom-swarming, which requires that...

We propose the outperformance probability as a new performance measure, which can be used in order to compare a strategy with a specified benchmark, and develop the basic statistical properties of its maximum-likelihood estimator in a Brownian-motion framework. The given results are used to...

This paper presents a brief review of interval-based hypothesis testing, widely used in bio-statistics, medical science, and psychology, namely, tests for minimum-effect, equivalence, and non-inferiority. We present the methods in the contexts of a one-sample t-test and a test for linear...

The aim of this work is to give an overview on nonlinear expectation and to relate them to other concepts that describe model uncertainty or imprecision in a probabilistic framework. We discuss imprecise versions of stochastic processes with a particular interest in imprecise Markov chains....

Recent studies show that loss probability (LP) is a decisive factor when people evaluate risk of assets in laboratory experiments, suggesting a positive relationship between LP and expected stock returns. This corresponds to the classical "Safety-First" principle. We find empirical support for...