New Paradigms in Mathematical Finance: Modeling, Analysis, Computation

The groundbreaking work of Black and Scholes (1973) on option pricing and its reformulation using stochastic integration by Harrison, Kreps and Pliska (1979, 1981) have turned mathematical finance into a playground of applied mathematics, in particular of stochastic analysis, statistics, optimization and numerical analysis. The recent financial and sovereign debt crisis, that have significantly and adversely affected the European Union and particularly Greece, have also had significant effects into the theory and practice of mathematical finance. They have led to a change of paradigm in several areas of the field, and the emergence of new and challenging mathematical questions.

Uncertainty, for example, concerns nowadays not only the outcome of the probabilistic model but also the choice of the model itself, leading to model-free methods in mathematical finance, while the risk-neutral valuation of derivatives has been complemented by different valuation adjustments, that quantify previously neglected (and negligible) risks. Simultaneously, recent advances in the statistical analysis of financial data have also led to a change of paradigm in financial modeling, with the introduction of the so-called rough volatility models. The present project deals with several important theoretical and applied facets of these emerging new paradigms.