Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 144-148. / by David Scott Greeley. / Ph.D.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 148-151. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Vita. / Includes bibliographical references. / by Philip David Hattis. / Ph.D.

Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / Bibliography: leaves 106-111. / M.S.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Chemistry. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 124-126. / by Paul Sclavounos. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 156-163. / by Chun Woon Lau. / Ph.D.

Tang, Sze Ki = 計算美式賣權的最優提早履約邊界及期權金 / 鄧思麒. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 96-102). / Abstracts in English and Chinese. / Tang, Sze Ki = Ji suan Mei shi mai quan de zui you ti zao lu yue bian jie ji qi quan jin / Deng Siqi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Black-Scholes Option Pricing Model --- p.1 / Chapter 1.1.1 --- Geometric Brownian Motion --- p.1 / Chapter 1.1.2 --- The Black-Scholes Equation --- p.3 / Chapter 1.1.3 --- The European Put Option --- p.5 / Chapter 1.1.4 --- The American Put Option --- p.7 / Chapter 1.1.5 --- Perpetual American Option --- p.9 / Chapter 1.2 --- Literature Review --- p.9 / Chapter 1.2.1 --- Direct Numerical Method --- p.10 / Chapter 1.2.2 --- Analytical Approximation --- p.11 / Chapter 1.2.3 --- Analytical Representation --- p.12 / Chapter 1.2.4 --- Mean-Reverting Lognormal Process --- p.13 / Chapter 1.2.5 --- Constant Elasticity of Variance Process --- p.15 / Chapter 1.2.6 --- Model Parameters with Time Dependence --- p.17 / Chapter 1.3 --- Overview --- p.18 / Chapter 2 --- Mean-Reverting Lognormal Model --- p.21 / Chapter 2.1 --- Moving Barrier Rebate Options under GBM --- p.21 / Chapter 2.2 --- Simulating American Puts under GBM --- p.25 / Chapter 2.3 --- Special Case: Time Independent Parameters --- p.26 / Chapter 2.3.1 --- Reduction to Ingersoll's Approximations --- p.26 / Chapter 2.3.2 --- Perpetual American Put Option --- p.28 / Chapter 2.4 --- Moving Barrier Rebate Options under MRL Process --- p.29 / Chapter 2.4.1 --- Reduction to Black-Scholes Model --- p.30 / Chapter 2.5 --- Simulating the American Put under MRL Process --- p.32 / Chapter 3 --- Constant Elasticity of Variance Model --- p.34 / Chapter 3.1 --- Transformations --- p.35 / Chapter 3.2 --- Homogeneous Solution on a Semi-Infinite Domain --- p.37 / Chapter 3.3 --- Particular Solution on a Semi-Infinite Domain --- p.38 / Chapter 3.4 --- Moving Barrier Options with Rebates --- p.39 / Chapter 3.5 --- Simulating the American Options --- p.40 / Chapter 3.6 --- Implication from the Special Case L = 0 --- p.41 / Chapter 4 --- Optimization for the Approximation --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- The Optimization Scheme --- p.44 / Chapter 4.2.1 --- Illustrative Examples --- p.44 / Chapter 4.3 --- Discussion --- p.45 / Chapter 4.3.1 --- Upper Bound of the Exact Early Exercise Price --- p.45 / Chapter 4.3.2 --- Tightest Lower Bound of the American Put Option Price --- p.48 / Chapter 4.3.3 --- Ingersoll's Early Exercise Decision Rule --- p.51 / Chapter 4.3.4 --- Connection between Ingersoll's Rule and Samuelson's Smooth Paste Condition --- p.51 / Chapter 4.3.5 --- Computation Efficiency --- p.52 / Chapter 4.4 --- Robustness Analysis --- p.53 / Chapter 4.4.1 --- MRL Model --- p.53 / Chapter 4.4.2 --- CEV Model --- p.55 / Chapter 4.5 --- Conclusion --- p.57 / Chapter 5 --- Multi-stage Approximation Scheme --- p.59 / Chapter 5.1 --- Introduction --- p.59 / Chapter 5.2 --- Multistage Approximation Scheme for American Put Options --- p.60 / Chapter 5.3 --- Black-Scholes GBM Model --- p.61 / Chapter 5.3.1 --- "Stage 1: Time interval [0, t1]" --- p.61 / Chapter 5.3.2 --- "Stage 2: Time interval [t1, T]" --- p.62 / Chapter 5.4 --- Mean Reverting Lognormal Model --- p.63 / Chapter 5.4.1 --- "Stage 1: Time interval [0, t1]" --- p.63 / Chapter 5.4.2 --- "Stage 2: Time interval [t1, T]" --- p.64 / Chapter 5.5 --- Constant Elasticity of Variance Model --- p.66 / Chapter 5.5.1 --- "Stage 1: Time interval [0, t1]" --- p.66 / Chapter 5.5.2 --- "Stage 2: Time interval [t1, T]" --- p.67 / Chapter 5.6 --- Duration of Time Intervals --- p.69 / Chapter 5.7 --- Discussion --- p.72 / Chapter 5.7.1 --- Upper Bounds for the Optimal Early Exercise Prices --- p.73 / Chapter 5.7.2 --- Error Analysis --- p.74 / Chapter 5.8 --- Conclusion --- p.77 / Chapter 6 --- Numerical Analysis --- p.79 / Chapter 6.1 --- Sensitivity Analysis of American Put Options in MRL Model --- p.79 / Chapter 6.1.1 --- Volatility --- p.79 / Chapter 6.1.2 --- Risk-free Interest Rate and Dividend Yield --- p.80 / Chapter 6.1.3 --- Speed of Mean Reversion --- p.81 / Chapter 6.1.4 --- Mean Underlying Asset Price --- p.83 / Chapter 6.2 --- Sensitivity Analysis of American Put Options in CEV Model --- p.85 / Chapter 6.2.1 --- Elasticity Factor --- p.87 / Chapter 6.3 --- American Options with time-dependent Volatility --- p.87 / Chapter 6.3.1 --- MRL American Options --- p.89 / Chapter 6.3.2 --- CEV American Options --- p.90 / Chapter 6.3.3 --- Discussion --- p.91 / Chapter 7 --- Conclusion --- p.94 / Bibliography --- p.96 / Chapter A --- Derivation of The Duhamel Superposition Integral --- p.101 / Chapter A.1 --- Time Independent Inhomogeneous Boundary Value Problem --- p.101 / Chapter A.2 --- Time Dependent Inhomogeneous Boundary Value Problem --- p.102

The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain. Therefore, spacetime problems can be studied as boundary value problems, where initial conditions are considered as part of the spacetime boundary conditions. When seeking solutions to these problems, it is natural to ask what are the correct spaces of functions to choose, to obtain wellposedness. This motivates the study of an abstract theory for unbounded partial differential operators associated with a general boundary value problem on a bounded domain. A framework for choosing the spaces is introduced, and conditions for the solvability of weak formulations are provided. We apply this framework to study wave problems on tents and to study wellposed discontinuous Petrov-Galerkin (DPG) formulations for the Schrödinger and wave equations. Several numerical issues are also discussed.

We solve initial boundary value problems with information unavailable at random time-steps. The randomly unavailable information represents asynchrony between processing elements. To approximate the initial boundary value problem, finite difference operators with summation-by-parts proper-ties and weak boundary procedures are used. Utilizing the energy method, we derive energy estimates for synchronous and asynchronous problems. The simulations show that the solutions may remain accurate and stable, even in the asynchronous case.