Free Access
Issue |
ESAIM: PS
Volume 19, 2015
|
|
---|---|---|
Page(s) | 515 - 543 | |
DOI | https://doi.org/10.1051/ps/2015001 | |
Published online | 16 November 2015 |
- N.H. Bingham and R. Kiesel, Risk-Neutral Valuation. Pricing and Hedging of Financial Derivatives. Springer Finance XVIII. Springer (2004). [Google Scholar]
- H. Cartan, Cours de calcul différentiel. Méthodes, Hermann (2007). [Google Scholar]
- T. Cass, C. Litterer and T. Lyons, Integrability Estimates for Gaussian Rough Differential Equations. Preprint: arXiv:1104.1813v3 (2011). [Google Scholar]
- P. Cheridito, Regularizing Fractional Brownian Motion with a View towards Stock Price Modeling. Ph.D. thesis, Université de Zürich (2001). [Google Scholar]
- L. Decreusefond and A. Ustunel, Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177–214. [CrossRef] [MathSciNet] [Google Scholar]
- T. Dieker, Simulation of Fractional Brownian Motion. Master thesis, University of Twente (2004). [Google Scholar]
- Y. El Khatib and N. Privault, Computations of Greeks in markets with jumps via the Malliavin calculus. Finance Stoch. 8 (2004) 161–179. [CrossRef] [MathSciNet] [Google Scholar]
- E. Fournié, J-M. Lasry, J. Lebuchoux, P.-L. Lions and N. Touzi, Applications of Malliavin calculus to Monte-Carlo methods in finance. Finance Stoch. 3 (1999) 391–412. [Google Scholar]
- P. Friz and N. Victoir, Differential equations driven by Gaussian signals. Ann. Inst. Henri Poincaré, Probab. Stat. 46 (2010) 369–341. [CrossRef] [MathSciNet] [Google Scholar]
- P. Friz and N. Victoir, Multidimensional Stochastic Processes as Rough Paths: Theory and Applications. Vol. 120 of Cambridge Stud. Appl. Math. Cambridge University Press, Cambridge (2010). [Google Scholar]
- E. Gobet and R. Münos, Sensitivity analysis using Itô–Malliavin calculus and martingales, and application to stochastic optimal control. SIAM J. Control Optim. 43 (2005) 1676–1713. [CrossRef] [MathSciNet] [Google Scholar]
- H. Kunita, Stochastic Flows and Stochastic Differential Equations. Vol. 24 of Cambridge Stud. Appl. Math.. Cambridge University Press, Cambridge (1997). [Google Scholar]
- D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliqué`a la finance, 2nd edition. Math. Appl. Ellipses (1997). [Google Scholar]
- A. Lejay, Controlled differential equations as Young integrals: A simple approach. J. Differ. Equ. 248 (2010) 1777–1798. [CrossRef] [Google Scholar]
- T. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998) 215–310. [CrossRef] [MathSciNet] [Google Scholar]
- T. Lyons and Z. Qian, System Control and Rough Paths. Oxford University Press (2002). [Google Scholar]
- P. Malliavin and A. Thalmaier, Stochastic Calculus of Variations in Mathematical Finance. Springer Finance. Springer-Verlag, Berlin (2006). [Google Scholar]
- B.B. Mandelbrot and J.W. Van Ness, Fractional Brownian motion, fractional noises and applications. SIAM Rev. 10 (1968) 422–437. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- N. Marie, A generalized mean-reverting equation and applications. ESAIM: PS 18 (2014) 799–828. [CrossRef] [EDP Sciences] [Google Scholar]
- N. Marie, Trajectoires rugueuses, processus gaussiens et applications. Probability [math.PR]. University Paul Sabatier, Toulouse III (2012) HAL: tel-00783931v2. [Google Scholar]
- A. Neuenkirch and I. Nourdin, Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. J. Theoret. Probab. 20 (2007) 871–899. [CrossRef] [MathSciNet] [Google Scholar]
- D. Nualart, The Malliavin Calculus and Related Topics, 2nd edition. Probab. Appl. Springer-Verlag, Berlin (2006). [Google Scholar]
- N. Privault and X. Wei, A Malliavin calculus approach to sensitivity in insurance. Insurance: Math. Econ. 35 (2004) 679–690. [CrossRef] [Google Scholar]
- L.C.G. Rogers, Arbitrage with fractional Brownian motion. Math. Finance 7 (1997) 95–105. [CrossRef] [MathSciNet] [Google Scholar]
- S. Samko, A. Kilbas and O. Marichev, Fractional Integrals and Derivatives. Gordon and Breach Science (1993). [Google Scholar]
- J. Teichmann, Calculating the Greeks by cubature formulas. Proc. Roy. Soc. London A 462 (2006) 647–670. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.