We study the martingale optimal transport duality for càdlàg processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of payoffs that includes American, Asian, Bermudan, and European options with intermediate maturity. We exhibit an optimal superhedging strategy for which the static part solves an auxiliary problem and the dynamic part is given explicitly in terms of the static part. In the case of finitely supported marginal laws, solving for the static part reduces to a semi-infinite linear program. This talk is based on joint work with Florian Stebegg (Columbia University).

I will explain how to understand the various structures that emerge in Liouville Quantum Gravity (which is the canonical way to define a random Markovian area measure in the plane) and its natural interplay with scaling limits of models from statistical mechanics, using some new special features that we derive in ongoing joint work with Jason Miller and Scott Sheeld. In particular, we will see that a CLE defined on an independent well-chosen LQG surface defines a Poisson point process of so-called quantum disks.

Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this talk, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index H ∈ (0, 1)). We rigorously establish a first order approximation of the optimal value, when the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by the zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this strategy in a specific family of admissible strategies. If time permits, we will also discuss the problem under fast mean-reverting fractional stochastic environment. Joint work with Ruimeng Hu (UCSB).

The Continuum Random Tree, introduced by Aldous in the 90’s, arises in numerous
different ways, for instance as the scaling limit of large uniform trees, via Brownian excursions, or
via a Poisson point processes. It carries a natural structure as a metric measure space and has
recently featured prominently in the LeGall’s and Miermont’s work on the Brownian map, as well
as Duplantier’s, Miller’s and Sheffield’s Brownian sphere. Beginning from basic definitions, I will
describe some of the highlights of this emerging theory such as connections to Liouville Quantum
Gravity, and will describe how to draw the CRT in the plane in a conformally natural way.

The 5th Berlin Workshop on Mathematical Finance for Young Researchers will take place from June 1-4, 2016.

The workshop, which is jointly organized by Humboldt University Berlin and Technical University Berlin, provides a forum for PhD students, postdoctoral researchers, and young faculty members from all over the world to discuss their research in an informal atmosphere.

Keynote lectures will be given by Kostas Kardaras (London), Steven Kou (Singapore), Ronnie Sircar (Princeton), and Josef Teichmann (Zurich).

Young researchers are invited to submit abstracts for contributed talks. The deadline for abstract submission is March 20, 2016. Notification of acceptance will be sent by March 31, 2016. For further information, abstract submission, and registration, please visit: http://www.math.hu-berlin.de/~mfy2016/

We hope to welcome many young researchers in Berlin!