Results 11 to 20 of about 24 (24)
Quasi‐shuffle algebras and renormalisation of rough differential equations
Bulletin of the London Mathematical Society, Volume 52, Issue 1, Page 43-63, February 2020., 2020 Abstract The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on rooted trees known from backward error analysis of B‐series. For this purpose, we present a so‐called arborification of the Hoffman–Ihara theory of quasi‐shuffle ...
Yvain Bruned +2 more
wiley +1 more source
An extension of the Clark‐Ocone formula
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 28, Page 1463-1476, 2004., 2004 A white noise proof of the classical Clark‐Ocone formula is first provided. This formula is proven for functions in a Sobolev space which is a subset of the space of square‐integrable functions over a white noise space. Later, the formula is generalized to a larger class of operators.
Said Ngobi, Aurel Stan
wiley +1 more source
Volterra equations with fractional stochastic integrals
Mathematical Problems in Engineering, Volume 2004, Issue 5, Page 453-468, 2004., 2004 Some fractional stochastic systems of integral equations are studied. The fractional stochastic Skorohod integrals are also studied. The existence and uniquness of the considered stochastic fractional systems are established. An application of the fractional Black‐Scholes is considered.
Mahmoud M. El-Borai +3 more
wiley +1 more source
Itô‐Skorohod stochastic equations and applications to finance
International Journal of Stochastic Analysis, Volume 2004, Issue 4, Page 359-369, 2004., 2004 We prove an existence and uniqueness theorem for a class of Itô‐Skorohod stochastic equations. As an application, we introduce a Black‐Scholes market model where the price of the risky asset follows a nonadapted equation.
Ciprian A. Tudor
wiley +1 more source
Transformations of index set for Skorokhod integral with respect to Gaussian processes
International Journal of Stochastic Analysis, Volume 12, Issue 2, Page 105-111, 1999., 1998 We consider a Gaussian process {Xt, t ∈ T} with an arbitrary index set T and study consequences of transformations of the index set on the Skorokhod integral and Skorokhod derivative with respect to X. The results applied to Skorokhod SDEs of diffusion type provide uniqueness of the solution for the time‐reversed equation and, to Ogawa line integral ...
Leszek Gawarecki
wiley +1 more source
Robust option replication for a Black‐Scholes model extended with nondeterministic trends
International Journal of Stochastic Analysis, Volume 12, Issue 2, Page 113-120, 1999., 1998 Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model. This memory or nondeterministic trend behavior is often seen as a reflection of market sentiments and causes that the historical volatility estimator becomes unreliable in practice.
John G. M. Schoenmakers +1 more
wiley +1 more source
A characterization and moving average representation for stable harmonizable processes
International Journal of Stochastic Analysis, Volume 9, Issue 3, Page 263-270, 1996., 1995 In this paper we provide a characterization for symmetric α‐stable harmonizable processes for 1 < α ≤ 2. We also deal with the problem of obtaining a moving average representation for stable harmonizable processes discussed by Cambanis and Soltani [3], Makegan and Mandrekar [9], and Cambanis and Houdre [2].
M. Nikfar, A. Reza Soltani
wiley +1 more source
Itô′s formula with respect to fractional Brownian motion and its application
International Journal of Stochastic Analysis, Volume 9, Issue 4, Page 439-448, 1996., 1996 Fractional Brownian motion (FBM) with Hurst index 1/2 < H < 1 is not a semimartingale. Consequently, the standard Itô calculus is not available for stochastic integrals with respect to FBM as an integrator if 1/2 < H < 1. In this paper we derive a version of Itô′s formula for fractional Brownian motion.
W. Dai, C. C. Heyde
wiley +1 more source
An approach to the stochastic calculus in the non‐Gaussian case
International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 361-370, 1995., 1995 We introduce and study a class of operators of stochastic differentiation and integration for non‐Gaussian processes. As an application, we establish an analog of the Itô formula.
Andrey A. Dorogovtsev
wiley +1 more source
Power variation of multiple fractional integrals
Open Mathematics, 2007 Tudor Constantin, Tudor Maria
doaj +1 more source