# Birgit Rudloff - Princeton University

**Starts:**3:30 pm on Tuesday, October 19, 2010

**Ends:**4:30 pm on Tuesday, October 19, 2010

**Location:**MCS 149

TITLE: Superhedging and risk measurement in multiasset models with transaction costs.
ABSTRACT: We consider a conical market model (generated, for example, by proportional transaction costs) and extend the notion of set-valued risk measures (Jouini, Meddeb, Touzi 2004, Hamel, Heyde 2010) to the case of random solvency cones at terminal time. This accounts for random exchange rates and/or random transaction costs. Several new features such as market compatibility will be discussed which do not appear (or are trivial) if the solvency cones are constant. It can be shown that in analogy to the frictionless case the superhedging price in markets with proportional transaction costs
(see e.g. Schachermayer 2004, Pennanen, Penner 2010) is a set-valued coherent risk measure, where the supremum in the dual representation is taken with respect to the set of equivalent martingale measures. Numerical examples will illustrate the theoretical results. Price bounds for market prices and the calculation of these price bounds and will be discussed. The superhedging price can be reduced by adding additional assets to the market.