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On pathwise stochastic integration

Author

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  • Karandikar, Rajeeva L.

Abstract

In this article, we construct a mapping : D[0, [infinity])xD[0,[infinity])-->D[0,[infinity]) such that if (Xt) is a semimartingale on a probability space ([Omega], , P) with respect to a filtration (t) and if (ft) is an r.c.l.l. (t) adapted process, then This is of significance when using stochastic integrals in statistical inference problems. Similar results on solutions to SDEs are also given.

Suggested Citation

  • Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
  • Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:11-18
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    References listed on IDEAS

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    1. Karandikar, Rajeeva L., 1983. "Stochastic integration w.r.t. continuous local martingales," Stochastic Processes and their Applications, Elsevier, vol. 15(2), pages 203-209, July.
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    Cited by:

    1. Neufeld, Ariel & Nutz, Marcel, 2014. "Measurability of semimartingale characteristics with respect to the probability law," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3819-3845.
    2. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org.
    3. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
    4. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    5. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    6. repec:eee:spapps:v:127:y:2017:i:12:p:3997-4028 is not listed on IDEAS
    7. Budhiraja, A., 2001. "Ergodic properties of the nonlinear filter," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 1-24, September.
    8. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
    9. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2016. "A superhedging approach to stochastic integration," Papers 1609.02349, arXiv.org, revised Sep 2017.
    10. Erhan Bayraktar & Song Yao, 2013. "On the Robust Optimal Stopping Problem," Papers 1301.0091, arXiv.org, revised Apr 2016.
    11. Amine Ismail & Huy^en Pham, 2016. "Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix ," Papers 1610.06805, arXiv.org, revised Mar 2017.
    12. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    13. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    14. Masaaki Fukasawa, 2012. "Efficient Discretization of Stochastic Integrals," Papers 1204.0637, arXiv.org.
    15. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.
    16. Keller, Christian & Zhang, Jianfeng, 2016. "Pathwise Itô calculus for rough paths and rough PDEs with path dependent coefficients," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 735-766.
    17. Bhatt, Abhay G. & Karandikar, Rajeeva L., 2002. "Robustness of the nonlinear filter: the correlated case," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 41-58, January.
    18. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1230-8 is not listed on IDEAS
    19. Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    20. B. Acciaio & M. Beiglbock & F. Penkner & W. Schachermayer & J. Temme, 2012. "A trajectorial interpretation of Doob's martingale inequalities," Papers 1202.0447, arXiv.org, revised Jul 2013.
    21. Dirk Becherer & Klebert Kentia, 2017. "Good Deal Hedging and Valuation under Combined Uncertainty about Drift and Volatility," Papers 1704.02505, arXiv.org.
    22. Buckdahn, Rainer & Ma, Jin & Zhang, Jianfeng, 2015. "Pathwise Taylor expansions for random fields on multiple dimensional paths," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2820-2855.
    23. Drapeau, Samuel & Heyne, Gregor & Kupper, Michael, 2015. "Minimal supersolutions of BSDEs under volatility uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2895-2909.
    24. Possamaï, Dylan, 2013. "Second order backward stochastic differential equations under a monotonicity condition," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1521-1545.

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