Towards the higher point holographic momentum space amplitudes

In this paper, we calculate higher point tree level vector amplitudes propagating in AdS$_4$. We use bulk perturbation theory to compute tree level Witten diagrams. We show that when these amplitudes are written in momentum space, they reduce to relatively simple expressions. We explicitly compute four and five point correlators and also sketch a general strategy to compute the full six-point correlators.Comment: 20 pages, 6 figures, minor typos corrected, journal versio

Martingale Optimal Transport and Robust Hedging in Continuous Time

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed