Related papers: Supremum penalizations for L\'{e}vy processes
We study the upper tail behaviors of the local times of the additive L\'{e}vy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L_2-norms of the…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
We discuss conditionings to avoid two points and one-point local time penalizations with conditioning to avoid another point, for which we adopt various clocks. We also give corrections to some of the previous results of Takeda--Yano for…
Monotone L\'evy processes with additive increments are defined and studied. It is shown that these processes have a natural Markov structure and their Markov transition semigroups are characterized using the monotone L\'evy-Khintchine…
We study a combination of the refracted and reflected L\'evy processes. Given a spectrally negative L\'evy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
Understanding the space-time features of how a L\'evy process crosses a constant barrier for the first time, and indeed the last time, is a problem which is central to many models in applied probability such as queueing theory, financial…
In this work, we consider moments of exponential functionals of L\'{e}vy processes on a deterministic horizon. We derive two convolutional identities regarding these moments. The first one relates the complex moments of the exponential…
Multistable L\'evy motions are extensions of L\'evy motions where the stability index is allowed to vary in time. Several constructions of these processes have been introduced recently, based on Poisson and Ferguson-Klass-LePage series…
The {\em drawdown} process $Y$ of a completely asymmetric L\'{e}vy process $X$ is equal to $X$ reflected at its running supremum $\bar{X}$: $Y = \bar{X} - X$. In this paper we explicitly express in terms of the scale function and the…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…
In this paper, we study the L\'evy process time-changed by independent L\'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive…
In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized…
In this paper we analyze the transient behavior of the workload process in a L\'evy input queue. We are interested in the value of the workload process at a random epoch; this epoch is distributed as the sum of independent exponential…
In this paper we analyze a L\'evy process reflected at a general (possibly random) barrier. For this process we prove Central Limit Theorem for the first passage time. We also give the finite-time first passage probability asymptotics.
Motivated by the pricing of lookback options in exponential L\'evy models, we study the difference between the continuous and discrete supremum of L\'evy processes. In particular, we extend the results of Broadie et al. (1999) to…
In this paper we present some limit theorems for power variation of L\'evy semi-stationary processes in the setting of infill asymptotics. L\'evy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving…
We study the extremal processes through Feller semigroups theory from which it is possible to observe some parallelism with subordinators. Consequently, we observe that an extremal process possesses concepts analogous to those of Laplace…