Computational Financial Mathematics Using MATHEMATICA®

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With the growing interest in mathematical methods for finance and trading, significant research is being conducted in universities and brokerage firms. This book offers a thorough overview of how mathematics, combined with Mathematica, can address financial problems. It presents sophisticated theories in a user-friendly manner, blending mathematical rigor with practical programming. The solution methods discussed include symbolic, numerical, and Monte Carlo approaches, all manageable with standard personal computers. No prior knowledge of Mathematica is necessary, as the book fully utilizes its symbolic, numeric, data management, and graphic capabilities. It explores Monte Carlo solutions for scalar and multivariable stochastic differential equations (SDEs) in the context of trading issues like Black-Scholes hedging. Additionally, it covers symbolic and numerical solutions for Black-Scholes and Dupire partial differential equations (PDEs) and offers fast numerical solutions to free boundary problems, detailing their implementation in Mathematica. A comprehensive analysis of optimal portfolio diversification is included, featuring an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics. This resource is tailored for academics and will also serve the practical needs of quantitatively minded professional and individual investors.