The Annals of Applied Probability

Brownian moving averages have conditional full support

Alexander Cherny

Full-text: Open access

Abstract

We prove that any Brownian moving average

Xt=−∞t (f(st)−f(s)) dBs,  t≥0,

satisfies the conditional full support condition introduced by Guasoni, Rásonyi and Schachermayer [Ann. Appl. Probab. 18 (2008) 491–520].

Article information

Source
Ann. Appl. Probab. Volume 18, Number 5 (2008), 1825-1830.

Dates
First available in Project Euclid: 30 October 2008

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1225372951

Digital Object Identifier
doi:10.1214/07-AAP502

Mathematical Reviews number (MathSciNet)
MR2432181

Zentralblatt MATH identifier
1151.91490

Subjects
Primary: 91B28
Secondary: 60G15: Gaussian processes

Keywords
Brownian moving average conditional full support Titchmarsh convolution theorem

Citation

Cherny, Alexander. Brownian moving averages have conditional full support. Ann. Appl. Probab. 18 (2008), no. 5, 1825--1830. doi:10.1214/07-AAP502. http://projecteuclid.org/euclid.aoap/1225372951.


Export citation

References

  • [1] Cheridito, P. (2001). Regularizing fractional Brownian motion with a view towards stock price modelling. Ph.D. thesis, ETH Zurich.
  • [2] Cherny, A. S. (2007). General arbitrage pricing model: Transaction costs. In Séminaire de Probabilités XL. Lecture Notes in Mathematics 1899 447–462. Springer, Berlin.
  • [3] Cvitanić, J., Pham, H. and Touzi, N. (1999). A closed-form solution to the problem of super-replication under transaction costs. Finance and Stochastics 3 35–54.
  • [4] Guasoni, P., Rásonyi, M. and Schachermayer, W. (2008). Consistent price systems and face-lifting pricing under transaction costs. Ann. Appl. Probab. 18 491–520.
  • [5] Kabanov, Yu. M. and Stricker, C. (2007). On martingale selectors of cone-valued processes. Preprint.
  • [6] Levental, S. and Skorokhod, A. V. (1997). On the possibility of hedging options in the presence of transaction costs. Ann. Appl. Probab. 7 410–443.
  • [7] Mandelbrot, B. and Van Ness, M. (1968). Fractional Brownian motions, fractional noises and applications. SIAM. Rev. 10 422–437.
  • [8] Soner, H. M., Shreve, S. E. and Cvitanić, J. (1995). There is no nontrivial hedging portfolio for option pricing with transaction costs. Ann. Appl. Probab. 5 327–355.
  • [9] Yosida, K. (1980). Functional Analysis. Springer, Berlin.