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Machine Learning in Quantitative Finance

Machine learning has revolutionized fields such as image, text, and speech recognition. There is now growing interest in applying machine learning in financial applications. Recently, we have developed machine learning methods for modeling high-frequency financial data, solving high-dimensional partial differential equations, and estimating continuous-time models. In particular, we analyze stochastic gradient descent in continuous time, which is an efficient algorithm for estimating continuous-time models from a continuous stream of data. We prove convergence, convergence rate, and central limit theorem results for this algorithm.ÌýThe analysis relies upon stochastic analysis and partial differential equation techniques.