Mathias Beiglböck

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We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a modelindependent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence of a traded option with a(More)
The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a(More)
In this paper we investigate model-independent bounds for exotic options written on a risky asset using infinite-dimensional linear programming methods. Based on arguments from the theory of MongeKantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we(More)
We present a unified approach to Doob’s Lp maximal inequalities for 1 ≤ p < ∞. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover our deterministic inequalities lead to new versions of Doob’s(More)
We consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and may possibly attain(More)
Let H be a countable subgroup of the metrizable compact abelian group G and f : H → T = R/Z a (not necessarily continuous) character of H . Then there exists a sequence (χn) ∞ n=1 of (continuous) characters of G such that limn→∞ χn(α) = f(α) for all α ∈ H and (χn(α)) ∞ n=1 does not converge whenever α ∈ G \ H . If one drops the countability and(More)
It is well known and not difficult to prove that if C ⊆ Z has positive upper Banach density, the set of differences C −C is syndetic, i.e. the length of gaps is uniformly bounded. More surprisingly, Renling Jin showed that whenever A and B have positive upper Banach density, then A − B is piecewise syndetic. Jin’s result follows trivially from the first(More)
We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a(More)
András Biró and Vera Sós prove that for any subgroup G of T generated freely by finitely many generators there is a sequence A ⊆ N such that for all β ∈ T we have (‖.‖ denotes the distance to the nearest integer) β ∈ G ⇒ ∑ n∈A ‖nβ‖ < ∞, β / ∈ G ⇒ lim sup n∈A,n→∞ ‖nβ‖ > 0. We extend this result to arbitrary countable subgroups of T. We also show that not(More)