Stochastic calculus with respect to continuous finite quadratic variation processes

By Francesco Russo, Pierre Vallois. 2000

160 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2b61bd8e316a025acd4be41477fd8fd13bc8eab4

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Citations in the corpus

Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations (2005, background): “In [36] the process 〈X, Y 〉 is called generalized covariation process; several properties are investigated in [37], [38], often in connection with the stochastic calculus introduced in [35].”
Some SDEs with distributional drift. (2004, methodology): “For convenience, we follow the framework of stochastic calculus introduced in [36] and continued in [37, 38, 39], [45, 46, 47] and [40].”
Itô's formula for a sub-fractional Brownian motion (2011, background): “Russo, F. and Vallois, P.: Elements of Stochastic Calculus via Regularization, Séminaire de Probabilités XL (2007), 147–185.”
A General Stochastic Calculus Approach to Insider Trading (2005, result): “We first recall the following result ([ 27 ]):”
Fractional stochastic differential equations with applications to finance (2013, methodology): “• The regularization approach was introduced by Russo and Vallois in [27, 28] and further developed by Cheridito and Nualart in [4].”
Elements of Stochastic Calculus via Regularization (2006, methodology): “Stochastic integration via regularization is a technique of integration developed in a series of papers by the authors starting from [45], continued in [46, 47, 48, 49, 44] and later carried out by other authors, among them [50, 11, 12, 54, 53, 55, 57, 16, 15, 17, 18, 23].”
Optimal portfolio for an insider in a market driven by Lévy processes (2006, background): “(For information on forward integrals with respect to Brownian motion see Nualart and Pardoux (1988), Russo and Vallois (1993, 1995, 2000) and Biagini and Øksendal (2005)).”
Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2003, methodology): “A concept of α-variation was already introduced in [39].”