arXiv subjects

Claus Griessler

Publications and source records attributed to Claus Griessler.

4 recordsLinked to original sources

arXiv2019

A land of monotone plenty

A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the multi-marginal version of the transport problem as well as in the martingale transport problem which arises from model-independent finance. We establish a unifying concept of c-monotonicity / finitistic optimality which describes the geometric structure of optimizers to infinite-dimensional linear programming problems. This allows us to strengthen known results in martingale optimal transport and the infinitely marginal case of the optimal transport problem. If the optimization problem can be formulated as a multi-marginal transport problem our contribution is parallel to a recent result of Zaev.

math.PR↗

arXiv2016

An extended footnote on finitely minimal martingale measures

This note contains a short discussion on the sufficiency of finite optimality in martingale transport. It is shown that finitely minimal martingale measures are solutions of the martingale transport problem when the cost function is upper semi-continuous and bounded from above by a sum of integrable functions. As an application a transparent proof of the uniqueness of left-monotone martingale transport plans is given.

math.PR↗

arXiv2016

$c$-cyclical monotonicity as a sufficient criterion for optimality in the multi-marginal Monge-Kantorovich problem

This note establishes that a generalization of $c$-cyclical monotonicity from the Monge-Kantorovich problem with two marginals gives rise to a sufficient condition for optimality also in the multi-marginal version of that problem. To obtain the result, the cost function is assumed to be bounded by a sum of integrable functions. The proof rests on ideas from martingale transport.

math.OC↗

arXiv2012

Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance dominates its quadratic variation in increasing convex order. The results have immediate applications to the pricing of options on realized variance. For a class of models including time-changed Levy models and Sato processes with symmetric jumps our results show that options on variance are typically underpriced, if quadratic variation is substituted for the discretely sampled realized variance.

q-fin.PR↗