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Mathematical Finance
Mathematical Finance 6.1I nterest and Effective Rates In this section, you will learn about various ways to solve simple and compound interest problems related to bank accounts and calculate the effective rate of interest. Upon completion you will be able to: • Apply the simple interest formula to various financial scenarios. • Apply the continuously compounded interest formula to various financial scenarios. • State the difference between simple interest and compound interest. • Use technology to solve compound interest problems, not involving continuously compound interest. • Compute the effective rate of interest, using technology when possible. • Compare multiple accounts using the effective rates of interest/effective annual yields. Working with Simple Interest It costs money to borrow money. The rent one pays for the use of money is called interest. The amount of money that is being borrowed or loaned is called the principal or present value. Interest, in its simplest form, is called simple interest and is paid only on the original amount borrowed. When the money is loaned out, the person who borrows the money generally pays a fixed rate of interest on the principal for the time period the money is kept. Although the interest rate is often specified for a year, annual percentage rate, it may be specified for a week, a month, or a quarter, etc. When a person pays back the money owed, they pay back the original amount borrowed plus the interest earned on the loan, which is called the accumulated amount or future value. Definition Simple interest is the interest that is paid only on the principal, and is given by I = Prt where, I = Interest earned or paid P = Present value or Principal r = Annual percentage rate (APR) changed to a decimal* t = Number of years* *The units of time for r and t must be the same. -
Math 581/Econ 673: Mathematical Finance
Math 581/Econ 673: Mathematical Finance This course is ideal for students who want a rigorous introduction to finance. The course covers the following fundamental topics in finance: the time value of money, portfolio theory, capital market theory, security price modeling, and financial derivatives. We shall dissect financial models by isolating their central assumptions and conceptual building blocks, showing rigorously how their gov- erning equations and relations are derived, and weighing critically their strengths and weaknesses. Prerequisites: The mathematical prerequisites are Math 212 (or 222), Math 221, and Math 230 (or 340) or consent of instructor. The course assumes no prior back- ground in finance. Assignments: assignments are team based. Grading: homework is 70% and the individual in-class project is 30%. The date, time, and location of the individual project will be given during the first week of classes. The project is mandatory; missing it is analogous to missing a final exam. Text: A. O. Petters and X. Dong, An Introduction to Mathematical Finance with Appli- cations (Springer, New York, 2016) The text will be allowed as a reference during the individual project. The following books are not required and may serve as supplements: - M. Capi´nski and T. Zastawniak, Mathematics for Finance (Springer, London, 2003) - J. Hull, Options, Futures, and Other Derivatives (Pearson Prentice Hall, Upper Saddle River, 2015) - R. McDonald, Derivative Markets, Second Edition (Addison-Wesley, Boston, 2006) - S. Roman, Introduction to the Mathematics of Finance (Springer, New York, 2004) - S. Ross, An Elementary Introduction to Mathematical Finance, Third Edition (Cambrige U. Press, Cambridge, 2011) - P. Wilmott, S. -
Mathematics and Financial Economics Editor-In-Chief: Elyès Jouini, CEREMADE, Université Paris-Dauphine, Paris, France; [email protected]
ABCD springer.com 2nd Announcement and Call for Papers Mathematics and Financial Economics Editor-in-Chief: Elyès Jouini, CEREMADE, Université Paris-Dauphine, Paris, France; [email protected] New from Springer 1st issue in July 2007 NEW JOURNAL Submit your manuscript online springer.com Mathematics and Financial Economics In the last twenty years mathematical finance approach. When quantitative methods useful to has developed independently from economic economists are developed by mathematicians theory, and largely as a branch of probability and published in mathematical journals, they theory and stochastic analysis. This has led to often remain unknown and confined to a very important developments e.g. in asset pricing specific readership. More generally, there is a theory, and interest-rate modeling. need for bridges between these disciplines. This direction of research however can be The aim of this new journal is to reconcile these viewed as somewhat removed from real- two approaches and to provide the bridging world considerations and increasingly many links between mathematics, economics and academics in the field agree over the necessity finance. Typical areas of interest include of returning to foundational economic issues. foundational issues in asset pricing, financial Mainstream finance on the other hand has markets equilibrium, insurance models, port- often considered interesting economic folio management, quantitative risk manage- problems, but finance journals typically pay ment, intertemporal economics, uncertainty less -
The Business Cycle and the Stock Market
-1- THE BUSINESS CYCLE AND THE STOCK MARKET by Andrei S leifer A.B., Harv d University (1982) SUBMITTED TO THE DEPARTMENT OF ECONOMICS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 1986 Andrei Shleifer 1986 The author hereby grants to M.I.T. permission to reproduce and to distribute copies of this thesis document in whole or in part. Signature of author__ Department of Economics May 12, 1986 Certified by Peter A. Diamond / Thesis Supervisor Certified by Franklin M. Fisher / Thesis Supervisor Accepted by Richard S. Eckaus Chairman, Departmental Graduate Committee ARCHIVES MASSACHUSETT SIN!TiTUTE OF TCHNN N1'' JUN 1 3 198E LIBRA";. - - 2 ABSTRACT The three essays of this thesis concern the role of expectations in determining the allocation of resources, particularly in the macroecono- mic context. Specifically, all three papers are motivated by the propo- sition that private agents' beliefs are aggregated into stock market prices, which can therefore influence the allocation of investment. The first essay does not deal with financial markets explicitly, although it explores the role of animal spirits in determining invest- ment. The essay describes an artificial economy, in which firms in dif- ferent sectors make inventions at different times, but innovate simultaneously to take advantage of high aggregate demand. In turn, high demand results from simultaneous innovation in many sectors. The economy exhibits multiple cyclical equilibria, with entrepreneurs' expectations determining which equilibrium obtains. These equilibria are Pareto ranked, and the most profitable equilibrium need not be the most effi- cient. -
Careers in Quantitative Finance by Steven E
Careers in Quantitative Finance by Steven E. Shreve1 August 2018 1 What is Quantitative Finance? Quantitative finance as a discipline emerged in the 1980s. It is also called financial engineering, financial mathematics, mathematical finance, or, as we call it at Carnegie Mellon, computational finance. It uses the tools of mathematics, statistics, and computer science to solve problems in finance. Computational methods have become an indispensable part of the finance in- dustry. Originally, mathematical modeling played the dominant role in com- putational finance. Although this continues to be important, in recent years data science and machine learning have become more prominent. Persons working in the finance industry using mathematics, statistics and computer science have come to be known as quants. Initially relegated to peripheral roles in finance firms, quants have now taken center stage. No longer do traders make decisions based solely on instinct. Top traders rely on sophisticated mathematical models, together with analysis of the current economic and financial landscape, to guide their actions. Instead of sitting in front of monitors \following the market" and making split-second decisions, traders write algorithms that make these split- second decisions for them. Banks are eager to hire \quantitative traders" who know or are prepared to learn this craft. While trading may be the highest profile activity within financial firms, it is not the only critical function of these firms, nor is it the only place where quants can find intellectually stimulating and rewarding careers. I present below an overview of the finance industry, emphasizing areas in which quantitative skills play a role. -
Financial Mathematics
Financial Mathematics Alec Kercheval (Chair, Florida State University) Ronnie Sircar (Princeton University) Jim Sochacki (James Madison University) Tim Sullivan (Economics, Towson University) Introduction Financial Mathematics developed in the mid-1980s as research mathematicians became interested in problems, largely involving stochastic control, that had until then been studied primarily by economists. The subject grew slowly at first and then more rapidly from the mid- 1990s through to today as mathematicians with backgrounds first in probability and control, then partial differential equations and numerical analysis, got into it and discovered new issues and challenges. A society of mostly mathematicians and some economists, the Bachelier Finance Society, began in 1997 and holds biannual world congresses. The Society for Industrial and Applied Mathematics (SIAM) started an Activity Group in Financial Mathematics & Engineering in 2002; it now has about 800 members. The 4th SIAM conference in this area was held jointly with its annual meeting in Minneapolis in 2013, and attracted over 300 participants to the Financial Mathematics meeting. In 2009 the SIAM Journal on Financial Mathematics was launched and it has been very successful gauged by numbers of submissions. Student interest grew enormously over the same period, fueled partly by the growing financial services sector of modern economies. This growth created a demand first for quantitatively trained PhDs (typically physicists); it then fostered the creation of a large number of Master’s programs around the world, especially in Europe and in the U.S. At a number of institutions undergraduate programs have developed and become quite popular, either as majors or tracks within a mathematics major, or as joint degrees with Business or Economics. -
ANDREI SHLEIFER 1 March 2019
ANDREI SHLEIFER 1 March 2019 ANDREI SHLEIFER Department of Economics Harvard University M9 Littauer Center Cambridge, MA 02138 Date of Birth: February 20, 1961 Citizenship: U.S.A. Undergraduate Studies: Harvard, A.B., Math, 1982. Graduate Studies: MIT, Ph.D., May, 1986. Thesis Title: “The Business Cycle and the Stock Market” EMPLOYMENT: John L. Loeb Professor of Economics, Harvard University, 1991 - present. Professor of Finance and Business Economics, Graduate School of Business, The University of Chicago, 1989 - 1990. Assistant Professor of Finance and Business Economics, Graduate School of Business, The University of Chicago, 1987 - 1989. Assistant Professor of Economics, Princeton University, 1986 - 1987. OTHER AFFILIATIONS: Faculty Research Fellow and Research Associate, National Bureau of Economic Research, 1986- Associate and Advisory Editor, Journal of Financial Economics, 1988 - . Associate Editor, Journal of Finance, 1988 - 1991. Editor, Quarterly Journal of Economics, 1989 - 1999, 2012 - Advisor, Government of Russia, 1991 - 1997. Principal, LSV Asset Management, 1994 - 2003. Editor, Journal of Economic Perspectives, 2003 - 2008. ANDREI SHLEIFER 2 March 2019 AWARDS, FELLOWSHIPS, AND GRANTS: National Science Foundation Graduate Fellowship, 1983 - 1986. CRSP Distinguished Visiting Scholar, Graduate School of Business, The University of Chicago, March-June, 1986. Alfred P. Sloan Fellowship, 1990. National Science Foundation Grants, 1988 - 1989, 1990 - 1991, 19 94 - 1996, 1998 - 2000, 2001 - 2003. Presidential Young Investigator Award, 1989 - 1994. Bradley Foundation Grant, 1989, 1990, 1991 - 1992. Russell Sage Foundation Grant (with R. Vishny), 1988, 1991. Alfred P. Sloan Foundation Grant (with L. Summers), 1986, 1988 - 1990. Fellow, Econometric Society, 1993. Roger F. Murray Award of the Q-Group, 1994, and the Smith-Breeden Prize of the Journal of Finance for Distinguished paper, 1995, given to “Contrarian Investment, Extrapolation, and Risk.” Member, U.S.-Israel Joint Economic Development Group, 1995 - 1997. -
Shleifer's Failure
Shleifer’s Failure THE FAILURE OF JUDGES AND THE RISE OF REGULATORS. By Andrei Shleifer. Cambridge, Massachusetts: MIT Press, 2012. 352 pages. $40.00. Reviewed by Jonathan Klick* I. Introduction Andrei Shleifer is undoubtedly among the world’s most important economists. By standard citation measures, no one else is anywhere close. For example, his nearly 19,000 citations in the RePEc rankings1 as of October 2012 place him ahead of Nobel Prize2 winners such as James Heckman (12,212),3 Joseph Stiglitz (11,431),4 and Robert Lucas (9,314).5 His work on corporate finance, behavioral finance, and transition economics earned him the American Economic Association’s prestigious John Bates Clark medal in 1999.6 Perhaps not even international scandal will keep Shleifer from taking his place among the Nobelists.7 Shleifer’s influence in legal scholarship is almost as large. With more than 1,000 Westlaw citations,8 Shleifer would compare favorably to most law and economics specialists in top U.S. law schools.9 Given all of this, the publication of Shleifer’s book The Failure of Judges and the Rise of Regulators10 as part of the MIT Press’s Walras-Pareto Lecture series is sure to be of interest to a wide range of legal scholars, students, and policy makers—and especially to those who do not have access to JSTOR11 and a * Professor of Law, University of Pennsylvania. 1. Top 5% Authors, as of October 2012, IDEAS, http://ideas.repec.org/top/top .person.nbcites.html. 2. Formally the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, NOBELPRIZE.ORG, http://www.nobelprize.org/nobel_prizes/economics, but only pedants note this, such as bloggers who disagree with a given Nobelist’s positions. -
NBER WORKING PAPER SERIES a NORMAL COUNTRY Andrei
NBER WORKING PAPER SERIES A NORMAL COUNTRY Andrei Shleifer Daniel Treisman Working Paper 10057 http://www.nber.org/papers/w10057 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 October 2003 We thank Anders Aslund, Olivier Blanchard, Maxim Boycko, David Cutler, Martin Feldstein, Sergei Guriev, Stephen Hanson, Simon Johnson, David Laibson, Dwight Perkins, Lawrence Summers, Judith Thornton, Katia Zhuravskaya, and participants at a seminar at the University of Washington. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. ©2003 by Andrei Shleifer and Daniel Treisman. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. A Normal Country Andrei Shleifer and Daniel Treisman NBER Working Paper No. 10057 October 2003 JEL No. P2, P3, P5 ABSTRACT During the 1990s, Russia underwent an extraordinary transformation from a communist dictatorship to a multi-party democracy, from a centrally planned economy to a market economy, and from a belligerent adversary of the West to a cooperative partner. Yet a consensus in the US circa 2000 viewed Russia as a disastrous and threatening failure, and the 1990s as a decade of catastrophe for its citizens. Analyzing a variety of economic and political data, we demonstrate a large gap between this perception and the facts. In contrast to the common image, by the late 1990s Russia had become a typical middle-income capitalist democracy. Andrei Shleifer Harvard University Department of Economics M9Littauer Center Cambridge, MA 02138 and NBER [email protected] Daniel Treisman University of California, Los Angeles Political Science Department 3265 Bunche Hall Los Angeles, CA 90095-1472 [email protected] 1 Introduction During the 1990s, Russia underwent an extraordinary transformation. -
Mathematical Finance MS and Ph.D. Course Requirements
Mathematical Finance M.S. and Ph.D. Course requirements Master of Science with a Specialization in Mathematical Finance The full-time program of study for the M.S. degree specializing in Mathematical Finance focuses on building a solid foundation in applied mathematics, uncovers models used in financial applications, and teaches computational tools for developing solutions. The M.S. degree consists of 36 hours of graduate work including 3 hours of credit for a departmental report or 6 hours of credit for the master’s thesis. Up to 3 hours of graduate work are permitted in other areas such as mathematics, statistics, business, economics, finance or fields as approved by the graduate advisor. M.S. students share core courses with beginning Ph.D. students. To enter the program of study leading to a Master of Science Degree specializing in Mathematical Finance, the applicant must meet the requirements of the Graduate School and of the Department of Mathematics and Statistics. The degree requirements are as follows. A. Completion of the following required courses. A.1 FIN 5328 - Options and Futures A.2 STAT 5328 - Mathematical Statistics I A.3 STAT 5329 - Mathematical Statistics II A.4 MATH 5399 (Special Topics) - Applied Time Series A.5 MATH 6351 - Quantitative Methods with Applications to Financial Data A.6 MATH 6353 - Stochastic Calculus with Applications to Financial Derivatives B. Completion of any two courses from the following elective list. B.1 STAT 5371 - Regression Analysis B.2 STAT 5386 - Statistical Computation and Simulation B.3 -
Can Higher Prices Stimulate Product Use? Evidence from a Field Experiment in Zambia
Can Higher Prices Stimulate Product Use? Evidence from a Field Experiment in Zambia Nava Ashraf James Berry Jesse M. Shapiro Working Paper 07-034 Copyright © 2006, 2007, 2008 by Nava Ashraf, James Berry, and Jesse M. Shapiro Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author. Can Higher Prices Stimulate Product Use? Evidence from a Field Experiment in Zambia Nava Ashraf James Berry Harvard Business School Massachusetts Institute of Technology Jesse M. Shapiro University of Chicago and NBER August 14, 2008 Abstract The controversy over whether and how much to charge for health products in the developing world rests, in part, on whether higher prices can increase use, either by targeting distribution to high-use households (a screening e¤ect), or by stimulating use psychologically through a sunk-cost e¤ect. We develop a methodology for separating these two e¤ects. We implement the methodology in a …eld experiment in Zambia using door-to-door marketing of a home water puri…cation solution. We …nd that higher prices screen out those who use the product less. By contrast, we …nd no consistent evidence of sunk-cost e¤ects. JEL classi…cation: C93, D12, L11, L31 Keywords: chlorination, water-borne diseases, sunk-cost e¤ect, non-pro…t strategy, social marketing We are grateful to Gary Becker, Stefano DellaVigna, Dave Donaldson, Erik Eyster, Matthew Gentzkow, Jerry Green, Ali Hortaçsu, Emir Kamenica, Dean Karlan, Larry Katz, Michael Kremer, Stephen Leider, Steve Levitt, John List, Kevin M. -
C:\Working Papers\7804.Wpd
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