The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes supermartingales , when deflated by it  . The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices,  the stable behavior of the numeraire portfolio is established when each of the aforementioned market parameters is changed in an infinitesimal way.
The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes , when deflated by it , supermartingales . The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, we establish the stable behavior of the numeraire portfolio when each of the aforementioned market parameters is changed in an infinitesimal way.
D
supermartingales
A
, supermartingales
A
we establish
D
is established