Walter Schachermayer

Learn More
We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov’s approach to foreign exchange markets under transaction costs. The financial market is modelled by a d × d matrix-valued stochastic process (Σt)t=0 specifying the mutual bid and ask prices between d assets. We introduce the notion of “robust no arbitrage”, which is a(More)
This paper accompanies a previous one [KS99] by D. Kramkov and the present author. While in [KS99] we considered utility functions U : R+ → R satisfying the Inada conditions U ′(0) = ∞ and U ′(∞) = 0, in the present paper we consider utility functions U : R → R which are finitely valued, for all x ∈ R, and satisfy U ′(−∞) =∞ and U ′(∞) = 0. A typical(More)
We show that if we allow general admissible integrands as trading strategies the three dimensional Bessel process Bes admits arbitrage possibilities This is in contrast with the fact that the inverse process is a local martingale and hence is arbitrage free This leads to some economic interpretation for the analysis of the property of arbitrage in foreign(More)
Uncertainty on the choice of an option pricing model can lead to “model risk” in the valuation of portfolios of options. After discussing some properties which a quantitative measure of model uncertainty should verify in order to be useful and relevant in the context of risk management of derivative instruments, we introduce a quantitative framework for(More)
This paper solves a long-standing open problem in mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is indeed possible if the dual(More)
S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterization of law invariant coherent risk measures, satisfying the Fatou property. The latter property was introduced by F. Delbaen [D 02]. In the present note we extend Kusuoka’s characterization in two directions, the first one being rather standard, while the second one is somewhat surprising.(More)
R. Dalang, A. Morton and W. Willinger have proved a beautiful version of the Fundamental Theorem of Asset Pricing which pertains to the case of nite discrete time: In this case the absence of arbitrage opportunities already characterizes the existence of an equivalent martingale measure. The purpose of this paper is to give an elementary proof of this(More)
We prove a general version of the super-replication theorem, which applies to Kabanov’s model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued càdlàg bid-ask process (Πt)t∈[0,T ] evolving in continuous time. We propose a new definition of admissible portfolio processes as predictable (not(More)