On the monotonicity principle of optimal Skorokhod embedding problem

In this paper, we provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established by Beiglb\"ock, Cox and Huesmann. This principle presents a geometric characterization that reflects the desired optimality properties of Skorokhod embeddings. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context together with a delicate application of the optional cross-section theorem and a clever conditioning argument

Optimal Skorokhod embedding under finitely-many marginal constraints

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod embedding problem to the case of finitely-many marginal constraints. Using the classical convex duality approach together with the optimal stopping theory, we obtain the duality results which are formulated by means of probability measures on an enlarged space. We also relate these results to the problem of martingale optimal transport under multiple marginal constraints

Tightness and duality of martingale transport on the Skorokhod space

The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time martingale transport on the Skorokhod space of cadlag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S-topology and the dynamic programming principle

Short- and long-term impact of remarkable economic events on the growth causes of China-Germany trade in agri-food products

This paper focuses on a systematic quantitative discussion of the short- and long-term impact of remarkable economic events on international trade in a two-stage framework. Firstly, procedures based on dummy variables are proposed to detect structural breaks, types and sizes of jumps caused by such events. Then we propose to apply a hierarchical CMS (Constant Market Share) model to all sub-periods defined by the detected change points to study the short- and long-term impact of those events on growth causes. Application to China-Germany trade in agri-food products shows that China’s accession to WTO had a negative short-term impact on corresponding series. But its long-term impact on China’s export competitiveness was definitely positive. The short-term impact of the EU’s CAP (Common Agricultural Policy) reform on Germany’s exports to China was also negative. Its long-term impact on export competitiveness was sometimes positive and sometimes negative. The financial crisis of 2008 caused a significant reduction of China’s agri-food exports to Germany. But Germany’s exports to China in 2009 were not affected by the financial crisis as much.Growth causes of agri-food trade; the CMS model; the EU’s CAP reform; China’s accession to WTO; financial crisis