Approximation at first and second order of -order integrals of the fractional Brownian motion and of certain semimartingales.
Approximation du crochet de certaines semimartingales continues
Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne
Approximation in law to the d-parameter fractional Brownian sheet based on the functional invariance principle.
We show a result of approximation in law of the d-parameter fractional Brownian sheet in the space of the continuous functions on [0,T]d. The construction of these approximations is based on the functional invariance principle.
Approximation martingale characterization of Wiener prcesses on locally compact abelian gorups.
Approximation of a symmetric α-stable Lévy process by a Lévy process with finite moments of all orders
In this paper we consider a symmetric α-stable Lévy process Z. We use a series representation of Z to condition it on the largest jump. Under this condition, Z can be presented as a sum of two independent processes. One of them is a Lévy process parametrized by x > 0 which has finite moments of all orders. We show that converges to Z uniformly on compact sets with probability one as x↓ 0. The first term in the cumulant expansion of corresponds to a Brownian motion which implies that can...
Approximation of convolutions by accompanying laws without centering.
Approximation of -processes by Gaussian processes.
Approximation of Lévy-Feller diffusion by random walk.
Approximation of predictable characteristics of processes with filtrations
Approximation of second-order moment processes from local averages.
Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet
A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters Finally, the approximation process is iterative on the quarter plane A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.
Approximation of the Snell envelope and american options prices in dimension one
We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.
Approximation of the Snell Envelope and American Options Prices in dimension one
We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.
Approximations et majorations optimales des statistiques d'ordre d'un échantillon
Approximations for the maximum of stochastic processes with drift
If a stochastic process can be approximated with a Wiener process with positive drift, then its maximum also can be approximated with a Wiener process with positive drift.
Arbitrage et lois de martingale
Arbitrage for simple strategies
Various aspects of arbitrage on finite horizon continuous time markets using simple strategies consisting of a finite number of transactions are studied. Special attention is devoted to transactions without shortselling, in which we are not allowed to borrow assets. The markets without or with proportional transaction costs are considered. Necessary and sufficient conditions for absence of arbitrage are shown.
Arbitrage in markets without shortselling with proportional transaction costs
We consider markets with proportional transaction costs and shortsale restrictions. We give necessary and sufficient conditions for the absence of arbitrage and also estimate the super-replication price.
Argumentwise invariant kernels for the approximation of invariant functions
We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Two subclasses of argumentwise kernels are considered, involving a fundamental domain or a double sum over orbits. We then derive invariance properties...