On martingale measures for stochastic processes with independent increments
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 1, pp. 87-100
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We consider a special semimartingale $X$ with independent increments and prove the existence and equivalence of a local martingale measure $\mathbf{P}^H$ for $X$, which minimizes the Hellinger process under the assumption that there exists an equivalent local martingale measure for $X$. This is done under the restriction of quasi-left-continuity and boundedness of jumps of $X$. Furthermore, we investigate the relation between the well-known minimal martingale measure $\mathbf{P}^{\min}$ and $\mathbf{P}^H$. It is shown that in a sense $\mathbf{P}^{\min}$ is an approximation of $\mathbf{P}^H$.
Keywords:
processes with independent increments, equivalent local martingale measure, minimal martingale measure, Hellinger process.
@article{TVP_1999_44_1_a5,
author = {P. Grandits},
title = {On martingale measures for stochastic processes with independent increments},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {87--100},
publisher = {mathdoc},
volume = {44},
number = {1},
year = {1999},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_1_a5/}
}
P. Grandits. On martingale measures for stochastic processes with independent increments. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 1, pp. 87-100. http://geodesic.mathdoc.fr/item/TVP_1999_44_1_a5/