Chloe Markovic
Dupire’s Equation and SPDEs: Theory, Financial Applications, and Corollary Results
Dupire’s PDE, and Stochastic Partial Differential Equations, are of great theoretical and practical interest, arising naturally in a number of problems. In particular, Dupire’s equation occurs in the study of volatility. It is related to the Black-Scholes Formula, used to calculate implicit volatility, and appears in the proof of other results in stochastics research.
There is, however, a current dearth of theoretical basis for it and related problems, from methods in harmonic analysis related to PDEs (in particular the adapted Ornstein-Uhlenbeck operator) , to the well-posedness of the problem, and theoretical results about the efficacy of machine learning systems in related practical use (i.e. number of neurons/layers required for a given level of accuracy). There is also potential to further extend its utility in the proof of other results, such as Strassen’s theorem. The project intends to research these questions and provide some new theoretical insight, as well as to implement resulting ideas into an algorithm for calculation of implicit volatility.
Chloe Markovic
Australian National University
Chloe Markovic is a mathematics student at the Australian National University in the PhB Science program. She has a broad range of academic interests within mathematics and further afield, but primarily focuses on harmonic analysis, stochastic analysis, and analytic number theory. She has a particular interest in financial mathematics (especially options pricing) as part of these fields, as well as systems modelling and optimisation. She finds immense satisfaction in the combination of collaboration and competition that can be found in research and elsewhere, having won numerous awards for her academic performance.
Outside of her studies she recharges and keeps up her competitive and creative spirit by hiking, cycling, advocacy and various design projects (3D printing, sewing, and fabrication).
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