Finite Element Methods in Financial Engineering: From Structural Mechanics to Digital Finance
English | August 31, 2026 | ASIN: B0HH8FTQQ6 | 1195 pages | Epub | 9.57 MB
A complete 32-chapter framework connecting finite element analysis, computational finance and modern digital markets.Finite Element Methods in Financial Engineering: From Structural Mechanics to Digital Finance brings together both volumes of the work in a single Kindle edition, moving from the mathematical foundations of finite element analysis to calibrated computational models for cryptocurrency derivatives and digital financial markets.Volume I develops the mathematical and numerical foundations: variational methods, weak formulations, function and approximation spaces, stability and convergence, Black-Scholes, stochastic volatility, jump dynamics, regularity, free-boundary problems, finite element construction, time discretisation, adaptive approximation and computational verification.Volume II moves from the verified numerical engine to computational finance and market applications. It develops calibration workflows, approximation-space experiments, Heston and Merton benchmarks, the Heston-Merton PIDE, Greeks and sensitivities, cryptocurrency derivative markets, perpetual futures and infinite-horizon pricing.A central theme of the book is Approximation Space Engineering: the deliberate selection and evaluation of finite-dimensional approximation spaces according to the mathematical structure of the pricing problem, the quantity of interest and the computational regime. Rather than assuming that one numerical representation is universally superior, the book examines how accuracy, stability, sensitivities and computational cost change across models and parameter regimes.The complete edition covers:• variational and finite element foundations• function spaces, regularity and convergence• Black-Scholes, Heston and Merton models• stochastic volatility and jump-diffusion pricing• Heston-Merton PIDE formulations• finite element implementation and verification• cryptocurrency option data and calibration• Greeks and sensitivity computation• adaptive and derivative-aware approximation spaces• perpetual cryptocurrency derivatives and funding• approximation-space experiments and regime maps• Approximation Space Adequacy and Approximation Space EngineeringWritten for researchers, quantitative-finance practitioners, computational scientists and advanced students, this complete Kindle edition presents the full progression from structural-mechanics-inspired finite element thinking to a unified numerical framework for contemporary computational and digital finance.Complete Kindle Edition · Volumes I-II · Chapters 1-32
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