Related papers: Parisian ruin probability for spectrally negative …
This paper investigates ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. We focus on joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
We study L\'{e}vy-like and truncated L\'{e}vy-like flights with step probability distribution of the form $r^{-1+\nu}$ for negative, positive, and zero $\nu$, focusing on the appearance of fractal geometry characteristics in the generated…
The purpose of this paper is to construct the law of a L\'evy process conditioned to avoid zero, under mild technicals conditions, two of them being that the point zero is regular for itself and the L\'evy process is not a compound Poisson…
In this article we get simple explicit formulas for $\Exp\sup_{s\leq t}X(s)$ where $X$ is a spectrally positive or negative L\'evy process with infinite variation. As a consequence we derive a generalization of the well-known formula for…
We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for…
We study the default risk in incomplete information. That means, we model the value of a firm by one L\'evy process which is the sum of brownian motion with drift and compound Poisson process. This L\'evy process can not be observed…
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation…
This paper considers magnitude, asymptotics and duration of drawdowns for some L\'{e}vy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative L\'{e}vy processes using an approximation…
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…
Given an autoregressive process X of order p (i.e. X_n = a_1 X_{n-1} + ...+ a_p X_{n_p} + Y_n where the random variables Y_1, Y_2, ... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a…
The L\'evy walk process for a lower interval of an excursion times distribution ($\alpha<1$) is discussed. The particle rests between the jumps and the waiting time is position-dependent. Two cases are considered: a rising and diminishing…
Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a L\'evy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In…
We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…
The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative L\'evy process \xi with unbounded variation.…
In this paper, we are concerned with the numerical solution of one type integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we will try to simulate the…
This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently…
We investigate the upper tail probabilities of the all-time maximum of a stable L\'evy process with a power negative drift. The asymptotic behaviour is shown to be exponential in the spectrally negative case and polynomial otherwise, with…
In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…
We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion.…