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Hedging under Friction and Uncertainty: Theory and Numerics

Final Report Summary - HEDGING (Hedging under Friction and Uncertainty: Theory and Numerics)

My goal in this project is to deal with a class of hedging and pricing problems arising in modern Mathematical Finance. These problems are not only interesting from the point of view of applications, but also provide a good source for new mathematical questions which require new tools in the area of Probability Theory. I focused on three main topics:
i. Hedging with Friction.
ii. Robust Hedging.
iii. Numerical Schemes.

All the above topics are related to theory of Pricing and Hedging of Derivative Securities. In real Market conditions,
it is very difficult to provide an accurate probabilistic model for the behaviour of stock prices. Furthermore, trading of assets is subject to transaction costs, i.e. there is a gap between the bid price and the ask price. These two facts raise the natural question of understanding hedging in markets with friction and model uncertainty.

During this project I wrote 9 papers, 8 already accepted/published and one more paper is under review.

The accepted/published papers appeared/will appear in top journals in mathematical finance such as
Annals of Applied Probability, Finance and Stochastics , Mathematical Finance and Mathematics of Operation Research.

In the written papers we (coauthors and me) developed a probabilistic theory for hedging problems in a non standard framework, which includes
model uncertainty and non continuous transaction costs. The written papers settled important questions and opened new research horizons in mathematical finance, in the direction of hedging under price impact and model uncertainty.

The impact of this project was an establishment (at the Hebrew University) of a research in the area of mathematical finance. Moreover, my collaboration relations with leading researchers will make an essential contribution to the scientific community in Israel,
and will strengthen the position of the Hebrew University in the field of mathematical finance.

Currently my research group contains, in addition to myself, two PhD students Benjamin Gotessman and Jonathan Zouari,
So far I had three Master Students that already graduated: Maxim Bocharenko, Chen Michael and Niv Nayman.

Moreover, I established several sources and seminars in mathematical finance.

Based on the described above achievements I received tenure and was promoted to Associate Professor.