Explore the intersection of deep learning and quantitative finance in this 59-minute seminar from the Fields Institute. Delve into the historical context of Hilbert's 13th problem and its relevance to modern machine learning techniques. Discover how continuous multivariate functions relate to deep neural networks and their application in solving stochastic differential equations for high-dimensional contingent claim valuation. Learn about Riskfuel's approach to pricing exotic options, including Bermuda swaptions and double knockout partial barrier options. Examine key principles such as the frequency principle, data placement strategies, and the trade-offs between network depth and width. Gain insights into the three pillars of Riskfuel and their innovative retraining methods for maintaining model accuracy.