Search Results - subject:"Stochastic integration"

Hyperfinite stochastic integration for Lévy processes with finite-variation jump part

Herzberg, Frederik - Institut für Mathematische Wirtschaftsforschung, … - 2008

This article links the hyperfinite theory of stochastic integration with respect to certain hyperfinite Lévy processes … with the elementary theory of pathwise stochastic integration with respect to pure-jump Lévy processes with finite …-variation jump part. Since the hyperfinite Itô integral is also defined pathwise, these results show that hyperfinite stochastic …

Persistent link: https://www.econbiz.de/10005227287

Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension

Strong, Winslow - In: Finance and Stochastics 18 (2014) 3, pp. 487-514

latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. The second purpose is to extend two …

Persistent link: https://www.econbiz.de/10010949749

Cylindrical fractional Brownian motion in Banach spaces

Issoglio, E.; Riedle, M. - In: Stochastic Processes and their Applications 124 (2014) 11, pp. 3507-3534

stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of …

Persistent link: https://www.econbiz.de/10011065087

On stochastic integration for volatility modulated Lévy-driven Volterra processes

Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Pedersen, Jan - In: Stochastic Processes and their Applications 124 (2014) 1, pp. 812-847

This paper develops a stochastic integration theory with respect to volatility modulated Lévy-driven Volterra (V MLV …

Persistent link: https://www.econbiz.de/10010719752

Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension

Strong, Winslow - In: Finance and stochastics 18 (2014) 3, pp. 487-514

Persistent link: https://www.econbiz.de/10010396056

A continuous time GARCH process driven by a Levy process: stationarity and second order behaviour

Klüppelberg, Claudia; Lindner, Alexander M.; Maller, Ross - 2005

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. Our COGARCH (continuous time GARCH) model, based on a single...

Persistent link: https://www.econbiz.de/10010275680

Stochastic integration with respect to the sub-fractional Brownian motion with H∈(0,12)

Shen, Guangjun; Chen, Chao - In: Statistics & Probability Letters 82 (2012) 2, pp. 240-251

We define a stochastic integral with respect to sub-fractional Brownian motion SH with index H∈(0,12) that extends the divergence integral from Malliavin calculus. For this extended divergence integral, we establish versions of the formulas of Itô and Tanaka that hold for all H∈(0,12).

Persistent link: https://www.econbiz.de/10011039984

Stationarity and second order behaviour of discrete and continuous time GARCH(1,1) processes

Klüppelberg, Claudia; Lindner, Alexander M.; Maller, Ross - 2003

We use a discrete time analysis, giver necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. The models, based on a single background driving Lévy process,...

Persistent link: https://www.econbiz.de/10010275681

Persistence and Nonstationary Models

McCabe, B.P.M.; Martin, G.M.; Tremayne, A.R. - Department of Econometrics and Business Statistics, … - 2003

The aim of this paper is to examine the measurement of persistence in a range of time series models nested in the framework of Cramer (1961). This framework is a generalization of the Wold (1938) decomposition for stationary time series which, in addition to accommodating the standard I(0) and...

Persistent link: https://www.econbiz.de/10005149028

Asymptotic behaviour of the density in a parabolic SPDE

Kohatsu, Arturo; Carreras, D. Márquez; Solé, M. Sanz - Department of Economics and Business, Universitat … - 1999

Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$. In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noise parameter is obtained. The...

Persistent link: https://www.econbiz.de/10005704885