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Collecting many methods that have previously been scattered in the literature, this book presents advanced techniques for solving high-dimensional nonlinear problems. Designed for practitioners, it is one of the first books to discuss nonlinear Black-Scholes partial differential equations (PDEs). The authors explain regression and dual methods for chooser options, the Monte Carlo approach for pricing the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection/particle method to calibrate local stochastic volatility, hybrid models to market vanilla options, and stochastic representations based on marked branching diffusions.