1st Edition
Foundations of Quantitative Finance, Book VII: Brownian Motion and Other Stochastic Processes
1. Brownian Motion - Existence
1.1 Introduction to Brownian Motion
1.2 Simplifications for Constructions of BM
1.3 Kolmogorov's Existence Theorem
1.4 Brownian Motion on (О, оо)
2. Constructions of Brownian Motion
2.1 Donsker's Theorem on (0, оо)
2.2 Levy's Construction on (0, 1)
2.3 Ciesielski's Construction on (0, 1)
2.4 Wiener's Construction on (0, 1)
3. Path Properties of Brownian Motion
3.1 Symmetry
3.2 Growth
3.3 Regularity
3.4 Variation
4. Markov Processes and Martingales
4.1 Markov Processes: Аn Introduction
4.2 Martingales: Аn Introduction
5. Markov and Diffusion Processes
5.1 Аn Equivalent Definition of Markov Process
5.2 Transition Measures of Stochastic Processes
5.3 Transition Measures of Markov Processes
5.4 Markov Transition Measures
5.5 General Markov Processes
5.6 Diffusion Processes
6. Stochastic Processes and Their Measurability
6.1 Brownian Motion Sample Spaces: А Recap
6.2 А Canonical Sample Space for Brownian Motion
6.3 The Natural and Other Filtrations on (S, o(S), µ)
6.4 Measurability of Stochastic Processes
6.5 Brownian Motion and the Usual Conditions
7. Martingales
7.1 Definition and Basic Properties
7.2 Regularization and Continuity Assumptions
7.3 Doob's Martingale Maximal Inequality 1
7.4 Doob's Martingale Maximal Inequality 2
7.5 Martingales and the Pricing of Financial Derivatives
8. Stopping Times and Local Martingales
8.1 Stopping Times
8.2 Stopped Processes and Local Martingales
8.3 Brownian Motion and the Strong Markov Property
9. Martingales and Local Martingales
9.1 Doob's Optional Stopping Theorems
9.2 Martingales vs. Local Martingales
9.3 Martingale Convergence
9.4 Doob's Optional Stopping Theorem 3
9.5 Identifying Martingales
Biography
Robert R. Reitano is Professor of the Practice in Finance at the Brandeis International Business School where he specializes in risk management and quantitative finance, and where he previously served as MSF Program Director, and Senior Academic Director. He has a Ph.D. in Mathematics from MIT, is a Fellow of the Society of Actuaries, and a Chartered Enterprise Risk Analyst. He has taught as Visiting Professor at Wuhan University of Technology School of Economics, Reykjavik University School of Business, and as Adjunct Professor in Boston University's Masters Degree program in Mathematical Finance. Dr. Reitano consults in investment strategy and asset/liability risk management, was Chief Investment Officer of Controlled Risk Insurance Company (CRICO), and previously had a 29-year career at John Hancock/Manulife in investment strategy and asset/liability management, advancing to Executive Vice President & Chief Investment Strategist. His research papers have appeared in a number of journals and have won an Annual Prize of the Society of Actuaries and two F.M. Redington Prizes awarded biennially by the Investment Section of the Society of the Actuaries. Dr. Reitano has served as Vice-Chair of the Board of Directors of the Professional Risk Managers International Association (PRMIA) and on the Executive Committee of the PRMIA Board, and is currently a member of the PRMIA Boston Steering Committee, the Financial Research Committee of the Society of Actuaries, and other not-for-profit boards and investment committees.
