Community Research and Development Information Service - CORDIS



Project ID: 335421
Funded under: FP7-IDEAS-ERC
Country: United Kingdom

Mid-Term Report Summary - ROBUSTFINMATH (Robust Financial Mathematics: model-ambiguous framework for valuation and risk management)

RobustFinMath Project focuses on developing a new approach to problems in mathematical finance which allows to quantify the impact and risks of making modelling assumptions. The proposed framework interpolates between two ends of the spectrum: the model-free and the model-specific approaches, both of which were pioneered in the seminal work of Merton (1973). Our overarching narrative is pathwise: we think of modelling assumptions as specifying the set of feasible paths for the future evolution of quantities of interest (e.g. price processes). The model free approach considers all paths to be possible and as such will not produce unique outputs but rather a set of feasible outputs (e.g. intervals of no-arbitrage prices). The model-specific approach narrows down the set of paths so that outputs become strongly constrained, or even unique as in the classical Black-Scholes model.

The project spans a wide range of interrelated questions and topics. We are interested both in studying important special cases, e.g. classes of widely traded financial derivates, as well as the general pricing and hedging theory applicable to abstract payoffs. We are simultaneously developing the modelling framework and the mathematical tools needed to underpin it. Our work focuses both on the discrete time and on the continuous time setups.

In discrete time we were able to build a complete theory which includes model-free and model-specific settings as special cases but allows to continuously interpolate between the two and is equipped with suitable versions of the Fundamental Theorem of Asset Pricing and the Pricing-Hedging duality describing the range of no-arbitrage prices and the associated efficient trading (hedging) strategies.

In continuous time, we obtained the pricing-hedging duality under a number of assumptions. These are satisfied under many realistic scenarios but more understanding is needed to develop abstract and fully general results. At the same time, we studied number of specific setups, often motivated by the most practically relevant settings. The ensuing contributions were varied in their focus and had a wide impact. The theoretical works in probability theory were published in the top journals such as the Annals of Probability and the Annals of Applied Probability and contributed in particular to the so-called iterated Skorokhod embedding problem and the pathwise understanding of martingale inequalities. Works in financial mathematics, but still with a theoretical focus, were published in the top journals such as Finance and Stochastics. Therein, we proposed, in particular, a robust approach to financial bubbles yielding an intrinsic justification to the popular class of mathematical models (the so-called strict local martingales). Finally, the more practically focused works analysed examples of robust modelling beliefs and the performance of the ensuing trading strategies. We looked at expressing beliefs on the future implied skew and trading those beliefs using data from the S&P500 options market.

The team has carried work and made significant mathematical contributions to many other related topics. The key example is the novel and exciting field of martingale optimal transportation but the range is much broader from pathwise stochastic integration with local times, classification of random times, enlargement of filtrations and pseudo-stopping times, through robust dynamically-consistent approach to portfolio optimisation (robust forward criteria) to behavioural finance with application to gambling modelling. Our papers have been published in leading international peer-reviewed journals in the respective fields and further work is being considered for publication. Team members have been invited to present our results at seminars and international conferences. We were also able to attract many leading researchers to visit us in Oxford.

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United Kingdom
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