Advances in Finance and Stochastics: Essays in Honour of by Freddy Delbaen (auth.), Klaus Sandmann, Philipp J.

By Freddy Delbaen (auth.), Klaus Sandmann, Philipp J. Schönbucher (eds.)

In many parts of finance and stochastics, major advances were made on the grounds that this box of study was once opened by means of Black, Scholes and Merton in 1973. Advances in Finance and Stochastics includes a choice of unique articles by means of a couple of hugely wonderful authors on examine themes which are at the moment within the concentration of curiosity of either teachers and practitioners. the themes span possibility administration, portfolio conception and multi-asset derivatives, industry imperfections, interest-rate modelling and unique options.

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Let h be a strictly positive IP'-integrable random variable. 6, then there is a 8 > 0 as well as a constant K such that for each set A of measure If[A] < 8 we can find an element 1 E P u such that lIf/hll oo :::; K. Proof. It does not do any harm to normalise the function h. We therefore may suppose that the measure dIP" = h dIf is a probability, equivalent to If. When working with the measure IP", the IP'-densities 1 E P u have to be replaced with the IP"-densities 1/h. The corollary is now a rephrasing of the theorem.

Insurance Math. , 1:41-53, 1982. 17. P. J. Savage. Application of the Radon-Nikodym theorem to the theory of sufficient statistics. Ann. Math. , 20:225-241, 1949. 18. S. Jaschke and U. Kuchler. Coherent risk measures, valuation bonds and (/-L, u) portfolio optimisation. defjaschke/papers/ (preliminary version), 1999. 19. Y. Kabanov. Hedging and liquidation under transaction costs in currency markets. Finance and Stochastics, 3:237-248, 1999. 20. J. Lindenstrauss. A short proof of Lyapounoff's theorem.

The core C(v), of the game v is the set of all finitely additive nonnegative measures Il E ba( D, F), such that Il( D) = v( D) and such that for all sets A E F we have Il(A) ~ v(A). The a-core, C" (v) is the set of all (J-additive measures in the core. Remark: In case the game v is absolutely continuous with respect to lP', it is easily seen that C(v) (resp. the a-core C"(v)) is actually a subset of ba(D,F,lP') (resp. £1(D,F,lP')). L E C(v) we necessarily have that Il(AC) ~ v(AC) = v(D). L(A) = O.

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