In a previous paper we proved that a necessary and sufficient condition for all martingales of a given filtration $(\mathscr{F}_t)$ to be continuous is that, for every stopping time $T$ and every $\mathscr{F}_T$-measurable random variable $X$, there exists a continuous local martingale $M$ with $M_T = X$ a.s. The aim of this paper is to study the following question: Can we choose $M \geq 0$ whenever $X \geq 0$? We also give a negative answer to Conjecture 7.1 of Harrison and Pliska.
Publié le : 1990-04-14
Classification:
Stochastic integral,
local martingale,
integral representation,
60G44,
60H05
@article{1176990848,
author = {Stricker, C.},
title = {Valeurs Prises par les Martingales Locales Positives Continues a un Instant Donne},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 626-629},
language = {fr},
url = {http://dml.mathdoc.fr/item/1176990848}
}
Stricker, C. Valeurs Prises par les Martingales Locales Positives Continues a un Instant Donne. Ann. Probab., Tome 18 (1990) no. 4, pp. 626-629. http://gdmltest.u-ga.fr/item/1176990848/