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Non-gaussian Merton-black-scholes Theory
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
Mathematical Finance
The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph. D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is considered as the starting point of modern finance as a mathematical discipline. On this remarkable anniversary the workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the state of the art. Apart from contributions to the known discrete, Brownian, and Lvy process models, first attempts to describe a market in a reasonable way by a fractional Brownian mo...
Computational Methods in Finance
Computational Methods in Finance is a book developed from the author’s courses at Columbia University and the Courant Institute of New York University. This self-contained text is designed for graduate students in financial engineering and mathematical finance, as well as practitioners in the financial industry. It will help readers accurately price a vast array of derivatives. This new edition has been thoroughly revised throughout to bring it up to date with recent developments. It features numerous new exercises and examples, as well as two entirely new chapters on machine learning. Features Explains how to solve complex functional equations through numerical methods Includes dozens of challenging exercises Suitable as a graduate-level textbook for financial engineering and financial mathematics or as a professional resource for working quants.
A Stochastic Control Framework for Real Options in Strategic Evaluation
The theoretical foundation for real options goes back to the mid 1980s and the development of a model that forms the basis for many current applications of real option theory. Over the last decade the theory has rapidly expanded and become enriched thanks to increasing research activity. Modern real option theory may be used for the valuation of entire companies as well as for particular investment projects in the presence of uncertainty. As such, the theory of real options can serve as a tool for more practically oriented decision making, providing management with strategies maximizing its capital market value. This book is devoted to examining a new framework for classifying real options f...
Algebras, Rings and Modules
Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.
