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Abstract: In this note, we study the infinite-dimensional conditional laws of Browniansemistationary processes. Motivated by the fact that these processes aretypically not semimartingales, we present sufficient conditions ensuring that aBrownian semistationary process has conditional full support, a propertyintroduced by Guasoni, R\-asonyi, and Schachermayer Ann. Appl. Probab., 182008 pp. 491-520. By the results of Guasoni, R\-asonyi, and Schachermayer,this property has two important implications. It ensures, firstly, that theprocess admits no free lunches under proportional transaction costs, andsecondly, that it can be approximated pathwise in the sup norm bysemimartingales that admit equivalent martingale measures.



Author: Mikko S. Pakkanen

Source: https://arxiv.org/



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