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Robust Financial Mathematics: model-ambiguous framework for valuation and risk management

Objective

"The last forty years have seen a remarkable interplay between Mathematics and contemporary Finance. At the heart of the successful growth of Mathematical Finance was a perfect fit between its dominant model--specific framework and the tools of stochastic analysis. However, this approach has always had important limitations, and the dangers of overreach have been illustrated by the dramatic events of the recent financial crisis.
I set out to create a coherent mathematical framework for valuation, hedging and risk management, which starts with the market information and not an a priori probabilistic setup. The main objectives are: (i) to incorporate both historical data and current option prices as inputs of the proposed robust framework, and (ii) to establish pricing-hedging duality, define the concept of no-arbitrage and prove a Fundamental Theorem of Asset Pricing, all in a constrained setting where the market information, and not a probability space, is fixed from the outset. Further, I will test the performance of robust valuation and hedging methods.
The project proposes a genuine change of paradigm. It requires building novel mathematical tools combining pathwise stochastic calculus, embedding problems, martingale optimal transport, variation inequalities as well as numerical methods.
Significant research efforts have focused on introducing and investigating a form of model uncertainty in Financial Mathematics. This project makes an important next step. Motivated by recent contributions, it builds a framework which consistently combines model ambiguity with a comprehensive use of market information. Further, it has built-in flexibility to interpolate between the model-specific and model-independent settings. It offers a new theoretical foundation opening horizons for future research. Moreover, it provides novel tools which could be applied by the financial industry."

Call for proposal

ERC-2013-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 218 639
Principal investigator
Jan Krzysztof Obloj (Dr.)
Administrative Contact
Gill Wells (Ms.)

Beneficiaries (1)

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
EU contribution
€ 1 218 639
Address
Wellington Square University Offices
OX1 2JD Oxford
Activity type
Higher or Secondary Education Establishments
Principal investigator
Jan Krzysztof Obloj (Dr.)
Administrative Contact
Gill Wells (Ms.)