Skip to main content
×
×
Home

Stochastic Integrals and Conditional Full Support

  • Mikko S. Pakkanen (a1)
Abstract

We present conditions that imply the conditional full support (CFS) property, introduced in Guasoni, Rásonyi and Schachermayer (2008), for processes Z := H + ∫K dW, where W is a Brownian motion, H is a continuous process, and processes H and K are either progressive or independent of W. Moreover, in the latter case, under an additional assumption that K is of finite variation, we present conditions under which Z has CFS also when W is replaced with a general continuous process with CFS. As applications of these results, we show that several stochastic volatility models and the solutions of certain stochastic differential equations have CFS.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Stochastic Integrals and Conditional Full Support
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Stochastic Integrals and Conditional Full Support
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Stochastic Integrals and Conditional Full Support
      Available formats
      ×
Copyright
Corresponding author
Postal address: Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FI-00014 Helsingin yliopisto, Finland. Email address: msp@iki.fi
References
Hide All
[1] Barndorff-Nielsen, O. E. and Shephard, N. (2001). Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. J. R. Statist. Soc. Ser. B 63, 167241.
[2] Bender, C., Sottinen, T. and Valkeila, E. (2008). Pricing by hedging and no-arbitrage beyond semimartingales. Finance Stoch. 12, 441468.
[3] Cheridito, P. (2001). Mixed fractional Brownian motion. Bernoulli 7, 913934.
[4] Cherny, A. (2008). Brownian moving averages have conditional full support. Ann. Appl. Prob. 18, 18251830.
[5] Comte, F. and Renault, E. (1998). Long memory in continuous-time stochastic volatility models. Math. Finance 8, 291323.
[6] Delbaen, F. and Schachermayer, W. (1995). The existence of absolutely continuous local martingale measures. Ann. Appl. Prob. 5, 926945.
[7] Dellacherie, C. and Meyer, P.-A. (1975). Probabilités et Potentiel. Hermann, Paris.
[8] Frey, R. (1997). Derivative asset analysis in models with level-dependent and stochastic volatility. CWI Quart. 10, 134.
[9] Gasbarra, D., Sottinen, T. and van Zanten, H. (2008). Conditional full support of Gaussian processes with stationary increments. Preprint 487, Department of Mathematics and Statistics, University of Helsinki.
[10] Guasoni, P., Rásonyi, M. and Schachermayer, W. (2008). Consistent price systems and face-lifting pricing under transaction costs. Ann. Appl. Prob. 18, 491520.
[11] Guo, X. (2001). An explicit solution to an optimal stopping problem with regime switching. J. Appl. Prob. 38, 464481.
[12] Jeulin, T. and Yor, M. (1979). Inégalité de Hardy, semimartingales, et faux-amis. In Séminaire de Probabilités XIII (Lecture Notes Math. 721), Springer, Berlin, pp. 332359.
[13] Kabanov, Y. and Stricker, C. (2008). On martingale selectors of cone-valued processes. In Séminaire de Probabilités XLI (Lecture Notes Math. 1934), Springer, Berlin, pp. 439442.
[14] Kallenberg, O. (2002). Foundations of Modern Probability, 2nd edn. Springer, New York.
[15] Kallianpur, G. (1971). Abstract Wiener processes and their reproducing kernel Hilbert spaces. Z. Wahrscheinlichkeitsth. 17, 113123.
[16] Millet, A. and Sanz-Solé, M. (1994). A simple proof of the support theorem for diffusion processes. In Séminaire de Probabilités XXVIII (Lecture Notes Math. 1583), Springer, Berlin, pp. 3648.
[17] Revuz, D. and Yor, M. (1999). Continuous Martingales and Brownian Motion, 3rd edn. Springer, Berlin.
[18] Rogers, L. C. G. and Williams, D. (2000). Diffusions, Markov Processes, and Martingales, Vol. 2. Cambridge University Press.
[19] Stroock, D. W. (1971). On the growth of stochastic integrals. Z. Wahrscheinlichkeitsth. 18, 340344.
[20] Stroock, D. W. and Varadhan, S. R. S. (1972). On the support of diffusion processes with applications to the strong maximum principle. In Proc. 6th Berkeley Symp. Mathematical Statistics and Probability, Vol. III, California Press, Berkeley, CA, pp. 333359.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed