We prove that for continuous stochastic processes S based on (Ω,F, P) for which there is an equivalent martingale measure Q0 with square-integrable density dQ0/dP, we have that the so-called `variance-optimal' martingale measure Qopt for which the density dQopt/dP has minimal L2(P)-norm is automatically equivalent to P. The result is then applied to an approximation problem arising in mathematical finance.
Publié le : 1996-03-14
Classification:
equivalent martingale measure,
mathematical finance,
optimal measure,
pricing by arbitrage,
representing measure,
risk-neutral measure
@article{1193758791,
author = {Delbaen, Freddy and Schachermayer, Walter},
title = {The variance-optimal martingale measure for continuous processes},
journal = {Bernoulli},
volume = {2},
number = {3},
year = {1996},
pages = { 81-105},
language = {en},
url = {http://dml.mathdoc.fr/item/1193758791}
}
Delbaen, Freddy; Schachermayer, Walter. The variance-optimal martingale measure for continuous processes. Bernoulli, Tome 2 (1996) no. 3, pp. 81-105. http://gdmltest.u-ga.fr/item/1193758791/