Talks (titles and abstracts)

Michael Kupper: Minimal Supersolutions of BSDEs and Model Uncertainty

We discuss the existence and uniqueness of minimal supersolutions of BSDEs under model uncertainty when the probability models are not dominated by a reference probability measure.
The talk is based on joint works with Samuel Drapeau and Gregor Heyne.

Jan Obloj: Beyond one marginal: on various ways to incorporate more information into the robust pricing and hedging

In this talk we discuss some of recent and ongoing work related to using market information to make robust framework more efficient. We give example of incorporating prices of call options for multiple maturities as well as some historic time series of prices. Links with some recent works on no-duality results are mentioned.

Bernt Øksendal: A stochastic control approach to duality and robust duality in finance

A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities:

(i) The optimal terminal wealth \(X*(T) : = X_{\phi*}(T)\) of the classical problem to maximise the expected U-utility of the terminal wealth \(X_{\phi}(T)\) generated by admissible portfolios \(\phi(t); 0 ≤ t ≤ T\) in a market with the risky asset price process modelled as a semimartingale

(ii) The optimal scenario \(dQ*/dP\) of the dual problem to minimise the expected V-value of \(dQ/dP\) over a family of equivalent local martingale measures \(Q\).
Here \(V\) is the convex dual function of the concave function \(U\).

(1) In the first part of this talk we consider markets modelled by Itô-Lévy processes, and we present a new approach to the above result in this setting, based on the maximum principle in stochastic control theory. An advantage with our approach is that it also gives an explicit relation between the optimal portfolio \(\phi*\) and the optimal scenario \(Q*\), in terms of backward stochastic differential equations. This is be used to obtain a general formula for the optimal portfolio \(\phi*(t)\) in terms of the Malliavin derivative.

(2) In the second part of the talk we extend this approach to study robust optimal portfolio problems and their (robust) dual.

We illustrate the results by examples.
The presentation is based on recent joint work with Agnès Sulem, INRIA-Rocquencourt, Paris.

Krzysztof Paczka: G-Lévy processes and robust optimization

In the talk I will present robust optimization using the G-Lévy process with finite activity living in the sublinear expectation space. The Itô calculus, Itô formula and (FB)SDE's will be introduced. At the end of the talk I will relate the control of FBSDE's driven by a G-Lévy process to the standard theory via the representation theorem for sublinear expectation.
Talk based on a research with An Ta (UiO).

Alex Schied: Trading under transient price impact

Based on an idealized model of a limit order book with resilience, Obizhaeva & Wang (2005) were the first to analyze optimal portfolio liquidation trajectories under transient price impact. Their original model has been generalized in several ways, e.g., so as to include nonlinear price impact, nonexponential resilience, multiple assets, or additional drift. In this talk, we will review some of these extensions and discuss the optimisation problems arising in the corresponding portfolio liquidation problems. Particular emphasis will be given to the role played by a drift in asset prices. It turns out that this latter problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. This has some consequences on a two-player situation.

Peter Spoida: Maximum Maximum of Martingales given Marginals and an Iteration of the Azema-Yor Embedding

We propose a robust superhedging strategy for simple barrier options, consisting of a portfolio of calls with different maturities and a self-financing trading strategy. The superhedging strategy is derived from a pathwise inequality. We illustrate how a stochastic control ansatz can provide a good guess for finding such strategies.
Under some additional assumption we construct a worst-case model - a solution to the Skorokhod embedding problem - hence demonstrating that our superhedge is the cheapest possible. A discussion of extensions of this embedding is provided.
The talk is based on joint work with Pierre Henry-Labordere, Jan Obloj and Nizar Touzi.

Agnès Sulem: Stochastic control under Model uncertainty and Forward-Backward Stochastic differential equations

 

Gregor Svindland: Pareto Optimal Allocations for Law-Invariant Robust Utilities

We prove the existence of Pareto optimal allocations if the involved agents have preferences in the class of probabilistic sophisticated variational preferences and thus choice criteria which correspond to law-invariant robust utilities.

An Thi Kieu Ta: Optimal stopping problem under ambiguity with jumps

In this paper we study an optimal stopping problem under ambiguity associated with jump-diffusion processes. We use a viscosity solution approach for the solution to HJB equality. We show how to use these results for search problems and American options.

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