DYNAMIC RISK MEASURES AND G-EXPECTATION

Choquet expectation and Peng’s g−expectation

In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng’s g-expectation. An open question has been, after making suitable restrictions to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficien...

Dynamic coherent risk measures

Banks and regulatory agencies use monetary measures of risk to assess the risk taken by financial investors; important examples are given by the so–called Value at Risk and the class of Coherent Risk Measures. The existing risk measures are of a static, one period nature. In practice, however, portfolios consist, of course, of a variety of different assets and derivatives with distinct maturiti...

Dynamic Bayesian Information Measures

This paper introduces measures of information for Bayesian analysis when the support of data distribution is truncated progressively. The focus is on the lifetime distributions where the support is truncated at the current age t>=0. Notions of uncertainty and information are presented and operationalized by Shannon entropy, Kullback-Leibler information, and mutual information. Dynamic updatings...

Time Consistent Dynamic Risk Measures

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 probabilit...