Abstract
In this article, we indicate that in any two-period model of financial
markets with a finite state space, we may define a variety of coherent
risk measures on the payoff space of the market. These risk measures
depend on the Equivalent or on the Generalized Equivalent Martingale
Measures of the market. We also present some examples which illustrate
the multiplicity of the coherent risk measures, which depends on
the extreme points of the set of the Generalized Martingale Measures
of a market, if this market is arbitrage free. We actually present in
a systematic way the previous connection jointly with the examples,
while the origins of these ideas come from the work of Artzner et al.
(1999). We also present an aspect of this connection related to the fi-
nite -dimensional Expected Shortfall, relying on the dual representation
of it and we provide arithmetic examples, too.
Mathematics Subject Classification: 32F18, 91B30
Keywords: (generalized) equivalent martingale measure; extreme points;
coherent risk measures