Jerome Combes-Knoke

Jerome Combes-Knoke has worked for our firm as an investment banker.  For his CURRENT resume, click here.  Other archival information on Mr. Combes-Knoke is found below.

Jerome at Carnegie Mellon University

Letter of Recommendation

Carnegie Mellon University Degrees  

Computational Finance (B.S.) + Economics (B.S.)

Jerome Combes-Knoke has been advised he is the only student in the history of Carnegie Mellon University to have completed BOTH a degree in Computational Finance AND Economics.  He was one of ten students selected to participate in the highly-competitive CMU Computational Finance, an interdepartmental blend providing depth in the triad of business, mathematics, and computer science.  Below are the courses completed to date.  Despite the heavy course load, he graduated on the "Dean's List with High Honors."  Below is selected coursework completed by Mr. Combes-Knoke:

MATHEMATICS:

21-120 Differential and Integral Calculus (10 units).  Functions, limits, derivatives, logarithmic, exponential, and trigonometric functions, inverse functions; L’Hospital’s Rule, curve sketching, Mean Value Theorem, related rates, linear and quadratic approximations, maximum-minimum problems, inverse functions, definite and indefinite integrals, and hyperbolic functions; applications of integration, integration by substitution and by parts.

21-122 Integration, Differential Equations, and Approximation (10 units).  Integration by trigonometric substitution and partial fractions; arc length; improper integrals; Simpson’s and Trapezoidal Rules for numerical integration; separable differential equations, first order linear differential equations, homogeneous second order linear differential equations with constant coefficients, series solution, Newton’s method, Taylor’s Theorem including a discussion of the remainder, sequences, series, power series.

21-126 Introduction to Mathematical Software (3 units).  This course provides an introduction to the use of several software packages, which are useful to mathematics students.  Among the packages are Maple and Mathematica for symbolic computing, TeX and LaTeX for mathematical documents, and Matlab for numerical computing.  The course will also introduce the mathematical facilities built into spreadsheets such as Excel.  The aim of the course is to provide the student with some basic skills in the use of this software without attempting complete coverage.  A deeper knowledge of the software will be easy to obtain after completing this course.

21-241 Matrix Algebra (9 units).  Vectors and matrices, the solution of linear systems of equations, vector spaces and subspaces, orthogonality, determinants, real and complex eigenvalues and eigenvectors, linear transformations.

21-256 Multivariate Analysis and Approximation (9 units).  Taylor’s Theorem; geometric sequences and series and their applications in compound interest; vectors and matrices, lines, and planes; partial derivatives, directional derivatives, gradient, chain rule, maximum-minimum problems, Lagrange multipliers and the Kuhn-Tucker Theorem.

21-260 Differential Equations (9 units).  Ordinary differential equations: first and second order equations, applications, Laplace transforms; partial differential equations: partial derivatives, separation of variables, Fourier series; systems of ordinary differential equations; applications.   

21-270 Introduction to Mathematical Finance (9 units).  The theme of this course is pricing derivative securities by replication.  The simplest case of this idea, static hedging, is used to discuss net present value of a non-random cash flow, internal rate of return, and put-call option parity.  Pricing by replication is then considered in a one-period random model.  Risk-neutral probability measures, the Fundamental Theorems of Asset Pricing, and an introduction to expected utility maximization and mean-variance analysis are presented in this model.  Finally, replication is studied in a multiperiod binomial model.  Within this model, the replicating strategies for European and American options are determined.

21-292 Operations Research (9 units).  Operations research offers a scientific approach to decision making, most commonly involving the allocation of scarce resources.  This course develops some of the fundamental methods used.  Linear programming: the simplex method and its linear algebra foundations, duality, post-optimality and sensitivity analysis; the transportation problem; the critical path method; non-linear programming methods.

21-370 Discrete Time Finance (9 units).  This course introduces the Black-Scholes option pricing formula, shows how the binomial model provides a discretization of this formula, and uses this connection to fit the binomial model to data.  It then sets the stage for Continuous-Time Finance by discussing in the binomial model the mathematical technology of filtrations, martingales, Markov processes and risk-neutral measures.  Additional topics are American options, expected utility maximization, the Fundamental Theorems of Asset Pricing in a multi-period setting, and term structure modeling, including the Heath-Jarrow-Morton model.  Students are expected to read and write proofs.

21-420 Continuous-Time Finance (9 units).  This course begins with Brownian motion, stochastic integration, and Ito’s formula from stochastic calculus.  This theory is used to develop the Black-Scholes option pricing formula and the Black-Scholes partial differential equation.  Additional topics may include models of credit risk, simulation, and expected utility maximization.

STATISTICS:

36-201 Statistical Reasoning and Practice (9 units).  This course will introduce students to the basic concepts, logic, and issues involved in statistical reasoning, as well as basic statistical methods used to analyze data and evaluate studies.  The major topics to be covered include methods for exploratory data analysis, an introduction to research methods, elementary probability, and methods for statistical inference.  The objectives of this course are to help students develop a critical approach to the evaluation of study designs, data and results, and to develop skills in the application of basic statistical methods in empirical research.  An important feature of the course will be the use of the computer to facilitate the understanding of important statistical ideas and for the implementation of data analysis.

36-225 Introduction to Probability and Statistics I (9 units).  Provides an introduction to probability and mathematical statistics for students in mathematics and statistics.  The use of probability theory is illustrated with examples drawn from engineering, the sciences, and management.  Topics include elementary probability theory, conditional probability and independence, random variables, distribution functions, joint and conditional distributions, law of large numbers, and the central limit theorem.

36-226 Introduction to Probability and Statistics II (9 units).  This course is the second half of a year long course in probability and mathematical statistics.  Topics include maximum likelihood estimation, confidence intervals, and hypothesis testing.  If time permits there will also be a discussion of linear regression and the analysis of variance.

36-410 Introduction to Probability Modeling (9 units).  An introductory-level course in stochastic processes.  Topics typically include Poisson processes, Markov chains, birth and death processes, random walks, recurrent events, and renewal theory.  Examples are drawn from reliability theory, queuing theory, inventory theory, and various applications in the social and physical sciences.

COMPUTER PROGRAMMING:

15-100 Introductory/Intermediate Programming (10 units).  An introduction to the process of program design and analysis using the Java programming language.  Topics to be covered include basic data types and their operators, I/O, control structures (selection, loops), classes (including methods and fields), arrays, and simple sorting and searching algorithms.

21-369 Numerical Methods (9 units).  This course provides an introduction to the use of computers to solve scientific problems.  Methods for the computational solution of linear algebra systems, nonlinear equations, the interpolation and approximation of functions, differentiation and integration, and ordinary differential equations.  Analysis of round-off and discretization errors and programming techniques.

BUSINESS & ECONOMICS:

70-122 Introduction to Accounting (9 units).  This course provides the knowledge and skills necessary for the student to understand financial statements and financial records and make use of the information for management and investment decisions.  Topics include an overview of financial statements and business decisions; the balance sheet, the income statement, and the cash flow statement; sales revenue, receivables, and cash; cost of goods sold and inventory; long-lived assets and depreciation, and amortization; current and long-term liabilities; owners’ equity; investments in other corporations; an introduction to financial statement analysis; and international issues dealing with financial statements.

70-365 International Trade and International Law (9 units).  The course discusses the international legal system and laws that affect international trade.  It covers the Foreign Corrupt Practices Act, treaties and concessions, shipping and customs, appointment of foreign sales agents, resolution of trade disputes, international mergers and joint ventures, international competition law, UN sales convention, international trade organizations (IMF, WTO, World Bank, etc.), risk insurance, cultural factors, international E-Commerce and intellectual property.

70-391 Finance (9 units).  The course examines the role of the financial manager in the overall management and control of a firm.  Stress is placed on the use of analytical models for improving the decision-making process.  Both the short-term management of working capital and the long-term planning of capital structure and investment strategy are covered.

73-100 Principles of Economics (9 units).  Literally, an introduction to economic principles, the goal of this course is to give students an understanding as to what constitutes good “economic thinking”.  This thought process is grounded in the construction and use of economics models.  Drawing on issues in both microeconomics and macroeconomics, fundamental principles are shown to transcend particular examples and allow the field to be seen as a coherent, unified whole.

73-200 Macroeconomics (9 units).  Through macroeconomic models built upon microeconomic foundations, insights are developed into economic growth processes and business cycles.  Topics include aggregation and measurement, national income, business cycle measurement, economic welfare theorems and social inefficiencies, the effect of government fiscal policy upon employment and productivity, and the relationship between investment, interest rates and economic growth.

73-226 Quantitative Economic Analysis (9 units).  Using and extending upon students’ introductory knowledge of probability and economic models, this course introduces students to the tools of economic analysis.  Taking the perspective of active economic participants (rather than outside observers), students gain experience with a diversity of analytical techniques--such as regression analysis and simulation--in the context of real world data decision problems.

73-251 Economic Theory (9 units).  This course prepares students for advanced coursework in economics by providing a mathematically intensive overview of economic theory.  Students take advantage of their knowledge of multi-dimensional calculus and constrained optimization techniques in order to understand the development and logical consistency of the most commonly employed economic models.  Topics include consumer preferences and utility function representations, consumer choice under a budget constraint, substitution and income effects, compensated and uncompensated demands, expected utility theory, risk and insurance, technology and production functions, cost minimization, profit maximizing firms, perfect competition, single-firm markets, game theoretic analysis of markets with few firms, introduction to general equilibrium models and the welfare laws.

73-347 Game Theory for Economists (9 units).  An introduction to the theory of non-cooperative games with an emphasis on economic applications.  After an initial examination of two-person, zero-sum games, the notion of a Nash equilibrium in an n-person, non-cooperative game is considered.  Existence of and refinements to the equilibrium concept are discussed in the context of both normal and extensive form games.  Economic applications may include various topics, including Cournot and Bertrand oligopoly models, general competitive exchange equilibrium, and free rider problems.

73-365 Industrial Organization (9 units).  This course is concerned with the economic analysis of industrial markets that are not perfectly competitive.  The effects of imperfect competition on firms’ decisions (pricing, location, advertising, research and development, among others) are reviewed.  Implications of these effects in terms of public policy are also discussed from a variety of perspectives.  Finally, applications to actual markets are considered.

73-372 International Money and Finance (9 units).  Course concerns itself with the determination of real, monetary, and financial aggregates and the policies that influence them in an international context.  Topics include: monetary policy and its effects on employment and inflation, the role of the banking system in the transmission of monetary policy, credit markets, banks as financial intermediaries, and the effect of domestic policies on international trade and financial markets.

BROADENING COURSEWORK:

99-102 Computing Skills Workshop (3 units).  The course is comprised of mostly Carnegie Mellon specific information and helps students understand what resources are available to them and what responsibilities they have as a user in our computing community.

33-106 Physics I for Engineering Students (12 units).  This is a first semester, calculus-based introductory physics course.  Basic principles of mechanics and thermodynamics are developed.  Topics include vectors, displacement, velocity, acceleration, force, equilibrium, mass, Newton’s laws, gravitation, work, energy, momentum, impulse, temperature, heat, equations of state, thermodynamic processes, heat engines, refrigerators, first and second laws of thermodynamics, and the kinetic theory of gases.

76-101 Interpretation and Argument (9 units).  This course will give students a comprehensive grounding in communication processes.  The class focuses on the way in which interpretive arguments in the processes of communication and social and personal development.  In the class, students will develop these skills by reading and understanding the important issues and arguments regarding those issues advanced by a variety of texts, both fiction and non-fiction.  They will then be asked to respond to these positions by developing positions of their own, in their writing and in their speaking.  The course thus serves as an introduction to the discourse and arguments of the academic community, as well as serving as an introduction to some of the broader issues that the academic community addresses.

79-104 Introduction to World History (9 units).  Course challenges students to think analytically about the major historical processes that shaped and continue to shape cultures and civilizations.  The course is based on a series of case studies that focus on shifting power relations between and within civilizations.  Three major themes connect the several topics discussed throughout the semester: issues of authority and inequality within civilizations; encounters and conflicts between civilizations; and patterns of continuity and change across space and time.  The course demonstrates how historians explain what has happened in the past and in various civilizations and cultures; presents the kinds of evidence that historians use to reconstruct the past; and examines the interpretations historians make based on this evidence.