Some representation theorems for invariant probability measures

Conditionally Invariant Probability Measures

V eronique Maume-Deschamps Section de Math ematiques, Universit e de Gen eve 2-4 rue du Lievre CP 240 Suisse. Abstract Let T be a measurable map on a Polish space X, let Y be a non trivial subset of X. We give conditions ensuring existence of conditionally invariant probability measures (to non absorption in Y). We also supply suucient conditions for these probability measures to be absolutely ...

Some Representation Theorems for Partially Ordered Sets

Central Limit Theorems for Law-Invariant Coherent Risk Measures

In this paper we study the asymptotic properties of the canonical plugin estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we first prove a central limit theorem for independent identically distributed data and then extend it to the case of weakly dependent ones. Finally, a number ...

Robust representation of convex risk measures by probability measures

Artzner, Delbaen, Eber and Heath ([1]) initialized a new direction to assess risks of financial positions by an axiomatic approach. It relies fundamentally on the concept of risk measures, which are functionals on sets of financial positions satisfying some basic properties. The convex risk measures are exactly those ones which guarantee that diversification does not increase the risk. From the...

Lasota-yorke Maps with Holes: Conditionally Invariant Probability Measures and Invariant Probability Measures on the Survivor Set

Let T : I ?! I be a Lasota-Yorke map on the interval I, let Y be a non trivial sub-interval of I and g 0 : I ?! R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to non absorption in Y. These conditions imply also...