On dynamic measures of risk

In the context of complete nancial markets, we study dynamic measures for the risk associated with a given liability C at time t = T , of the form (x; C) := sup 2D inf ()2A(x) S 0 (T) + : Here x is the initial capital available at time t = 0, A(x) the class of admissible portfolio strategies, S 0 () the price of the risk-free instrument in the market, P = fP g 2D a suitable family of probability measures, and 0; T ] the temporal horizon during which all economic activity takes place. The classes A(x) and D are general enough to incorporate margin requirements, and uncertainty about the actual values of stock-appreciation rates, respectively. For this latter purpose we discuss, in addition to the above \max-min" approach, a related measure of risk in a \Bayesian" framework. Risk-measures of this type were introduced by Artzner, Delbaen, Eber and Heath in a static setting, and were shown to possess certain desirable \coherence" properties.