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ISBN: 981461968X Year: 2015 Publisher: New Jersey : World Scientific,
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Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H. Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available. Extensive numerical simulations are carried out with the method of lines to examine the influence of the finite computational domain and of the chosen boundary conditions on option and bond prices in one and two dimensions, reflecting multiple assets, stochastic volatility, jump diffusion and uncertain parameters. Special emphasis is given to early exercise boundaries, prices and their derivatives near expiration. Detailed graphs and tables are included which may serve as benchmark data for solutions found with competing numerical methods.
Derivative securities --- Options (Finance) --- Bonds --- Discrete-time systems. --- Differential equations, Partial. --- Mathematical models.
ISBN: 0674010442 0674025768 0674045076 9780674045071 9780674010444 Year: 2022 Publisher: Cambridge, MA
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A compact exposition of optimal control theory and applications, which presents an elementary yet rigorous proof of the maximum principle and a way of applying the principle that should enable students to solve any one-dimensional problem routinely.
National wealth --- Economics --- Mathematical optimization --- Maximum principles (Mathematics) --- National income --- Wealth --- Economic development --- Mathematical models --- Accounting --- Mathematical optimization. --- Mathematical models. --- Accounting. --- AA / International- internationaal --- 305.976 --- 339.10 --- Algoritmen. Optimisatie. --- Raming van het goederenbezit en van het inkomen: algemeenheden. --- Maximum principles (Mathematics). --- E-books --- Growth models (Economics) --- Affluence --- Distribution of wealth --- Fortunes --- Riches --- Business --- Finance --- Capital --- Money --- Property --- Well-being --- National accounting --- National income accounting --- Income accounting --- Social accounting --- Differential equations, Partial --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Economics, Mathematical --- Numerical solutions --- Algoritmen. Optimisatie --- Raming van het goederenbezit en van het inkomen: algemeenheden --- Economics - Mathematical models --- National income - Accounting --- Wealth - Mathematical models --- Economic development - Mathematical models
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