Brownian semistationary processes and conditional full support

Details Brownian semistationary processes and conditional full support Brownian semistationary processes and conditional full support

2010-02-25

arxiv.org/abs/1002.4774v1

International Journal of Theoretical and Applied Finance 2011, Vol. 14, No. 4, 579-586

Mathematics

Probability

7 pages

Scientific paper

10.1142/S0219024911006747

In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian semistationary process has conditional full support, a property introduced by Guasoni, R\'asonyi, and Schachermayer [Ann. Appl. Probab., 18 (2008) pp. 491--520]. By the results of Guasoni, R\'asonyi, and Schachermayer, this property has two important implications. It ensures, firstly, that the process admits no free lunches under proportional transaction costs, and secondly, that it can be approximated pathwise (in the sup norm) by semimartingales that admit equivalent martingale measures.

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