Probability and Stochastic Analysis - University of Bonn
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Model independent finance and martingale optimal transport

Time:Mo. 8-10
Room:SR 1.008

Exam: 26./27. July; 1./2. September, (please sign up in office 3.029 until July 19th)

Description: 

One of the fundamental problems in mathematical finance is to give a fair price for the payoff of an exotic option given the evolution of the underlying X.

In model independent finance one is interested in worst case scenarios, i.e. upper and lower price bounds for the exotic option, given only partial information on the underlying X. For instance one only knows the price of a finite set of options or one knows the distribution of X at certain time instances. Mathematically, the latter can be understood as an optimal transport problem with the additional constraint that the coupling needs to be a martingale.

In the first part of this lecture we will consider these problems in discrete time covering a robust version of the fundamental theorem of asset pricing, duality and characterisation of optimisers for the martingale optimal transport problem, and applications to martingale inequalities among other things.

In the second part of the lecture we will deal with the continuous time problem and especially its beautiful connection to the classical Skorokhod embedding problem. Towards the end of the lecture, we will give an outlook on the current challenges of this field like extensions to multiple dimensions and multiple periods.

lecture notes


Prerequisites:

A solid background in stochastic analysis and measure theory is desirable. Prior knowledge of mathematical finance is helpful but not strictly required.

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