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• Intro
• Contents
• Preface
• Discrete Time
• 1. Martingales and Optimal Stopping
• 1.1 Lecture
• 1: Conditional expectations and martingales
• 1.1.1 Conditional expectation
• 1.1.2 Martingales, submartingales and supermartingales
• 1.1.3 Supermartingale decomposition
• 1.1.4 Stopping times, local martingales and martingale transform
• 1.2 Lecture
• 2: Optional sampling, martingale inequalities and upcrossings
• 1.2.1 Optional sampling (stopping) theorem
• 1.2.2 Martingale inequalities
• 1.2.3 Martingale convergence theorem
• 1.3 Lecture
• 3: Optimal stopping
• 1.3.1 Single player

• 1.3.2 Dynkin stopping games
• 1.4 Exercises
• 2. Derivatives in General and Binomial Markets
• 2.1 Lecture
• 4: Derivatives in discrete time markets
• 2.1.1 General financial market in discrete time
• 2.1.2 Derivative securities
• 2.2 Lecture
• 5: Pricing derivatives in binomial markets
• 2.2.1 Cox-Ross-Rubinstein (CRR) (binomial) market model
• 2.2.2 A martingale representation lemma
• 2.2.3 Fair price of options in CRR market
• 2.3 Exercises
• 3. Fundamental Theorems of Asset Pricing
• 3.1 Lecture
• 6: Arbitrage and completeness
• 3.1.1 Arbitrage
• 3.1.2 Counterexamples

• 3.1.3 Complete and incomplete markets
• 3.2 Appendices to Lecture
• 6: Finite sample space, general closedness and separation theorems
• 3.2.1
• Appendix 1: Finite sample space
• 3.2.2
• Appendix 2: A closedness theorem
• 3.2.3
• Appendix 3: Separation
• 3.3 Exercises
• 4. Superhedging
• 4.1 Lecture
• 7: Optional decomposition
• 4.1.1 Optional decomposition theorem
• 4.1.2 Supermartingales with respect to all martingale measures
• 4.2 Lecture
• 8: Superhedging in incomplete markets
• 4.2.1 Superhedging of European contingent claims in incomplete markets

• 4.2.2 Superhedging of American contingent claims
• 4.2.3 Superhedging of Israeli (game) contingent claims
• 4.2.4 Existence of a superhedging strategy for game options with the initial capital equal to the superhedging price
• 4.2.5 Pricing of contingent claims from buyer's point of view
• 4.3 Exercises
• 5. Hedging with Risk
• 5.1 Lecture
• 9: Partial hedging or hedging with risk
• 5.1.1 Quantile hedging
• 5.1.2 Minimizing the shortfall risk
• 5.1.3 Komlos theorem
• 5.2 Lecture
• 10: Shortfall risk minimization for game options
• 5.3 Exercises
• Continuous Time

• 6. Martingales in Continuous Time and Optimal Stopping
• 6.1 Lecture
• 11: Optional stopping and submartingale decomposition
• 6.1.1 Martingales in continuous time
• 6.1.2 Optional stopping (sampling) theorem and martingale inequalities
• 6.1.3 The Doob-Meyer decomposition
• 6.2 Lecture
• 12: Optimal stopping in continuous time
• 6.2.1 Single player
• 6.2.2 Dynkin games in continuous time
• 6.3 Exercises
• 7. Introduction to Stochastic Analysis
• 7.1 Lecture
• 13: Brownian motion
• 7.1.1 De nition and a direct construction

Rigorous mathematical finance relies strongly on two additional fields: optimal stopping and stochastic analysis. This book is the first one which presents not only main results in the mathematical finance but also these 'related topics' with all proofs and in a self-contained form. The book treats both discrete and continuous time mathematical finance. Some topics, such as Israeli (game) contingent claims, and several proofs have not appeared before in a self-contained book form. The book contains exercises with solutions at the end of it and it can be used for a yearlong advanced graduate course for mathematical students.
(source: Nielsen Book Data)

In recent years the finance industry has mushroomed to become an important part of modern economies, and many science and engineering graduates have joined the industry as quantitative analysts, with mathematical and computational skills that are needed to solve complex problems of asset valuation and risk management. An important parallel story exists of scientific endeavour. Between 1965-1995, insightful ideas in economics about asset valuation were turned into a mathematical 'theory of arbitrage', an enterprise whose first achievement was the famous 1973 Black-Scholes formula, followed by extensive investigations using all the resources of modern analysis and probability. The growth of the finance industry proceeded hand-in-hand with these developments. Now new challenges arise to deal with the fallout from the 2008 financial crisis and to take advantage of new technology, which has revolutionized the practice of trading. This Very Short Introduction introduces readers with no previous background in this area to arbitrage theory and why it works the way it does. Illuminating pricing theory, Mark Davis explains its applications to interest rates, credit trading, fund management and risk management. He concludes with a survey of the most pressing issues in mathematical finance today. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
(source: Nielsen Book Data)

• Front Cover; A Spiral Approach to Financial Mathematics; Copyright Page; Contents; Preface; Why the Changes in Content Sequencing?; What About Changes in Pedagogy?; Student Audience and How to Utilize the Materials; Students Hoping to Gain a Solid Understanding of Financial Mathematics Concepts; Students Hoping to Pass Actuarial Certification Exam FM; To All Students; To the Actuary Student; Unit 1 Introduction to Financial Mathematics;
• 1. Savings: Fundamentals of Interest; Section 1.1. Simple and compound interest; Learning objectives; Example 1.1. Saving Money to Study Abroad

• Interest over longer periodsExploration 1.1. Saving for Your First Car; Interest over longer periods; Turning to technology: Excel; Summary; Homework Questions: Section 1.1; Conceptual questions; Practice questions; Application questions; Looking ahead; Section 1.2. Changing the Compounding Period: Nominal vs Effective Interest Rates; Learning objectives; Example 1.2. Saving Money to Study Abroad (Revisited); Nominal versus effective interest rates; Back to the saving for study abroad example; Exploration 1.2. Saving for Your First Car (Revisited)

• Changing the period over which interest Is computedNominal versus effective interest rates; Back to the car example; Summary; Homework Questions: Section 1.2; Conceptual questions; Practice questions; Application questions; Looking ahead; Section 1.3. Valuing Accounts with Multiple Transactions; Learning objectives; Example 1.3. Saving for a Down Payment on a House; Basic account chart; Creating a dynamic account chart using Excel; What if you saved 900/month instead?; How much would you need to save each month to reach your goal within 18 months?; What about an extra deposit?

• Exploration 1.3. Saving for CollegeGetting started; Basic account chart for college savings; Begin filling in the account chart; Revisiting nominal rates of interest; Creating a dynamic account chart using Excel; Summary; Homework Questions: Section 1.3; Conceptual questions; Practice questions; Application questions; Looking ahead; Section 1.4. Tips and Tricks for Solving Cash Flow Problems; Learning objectives; Example 1.4. Saving for a Down Payment (Revisited); Nonrecursive approach; Evaluating the impact of a withdrawal; Irregular payments and withdrawals

• Problems involving an unknown interest rateProblems involving an unknown time period; Exploration 1.4. Saving for College (Revisited); Recursive approach; Nonrecursive approach; Irregular payments and withdrawals; Problems involving an unknown interest rate; Problems involving an unknown time period; Summary; Homework Questions: Section 1.4; Conceptual questions; Practice questions; Application questions; Looking ahead; End of chapter summary; End of chapter review problems;
• 2. Loans: Fundamentals of Borrowing and Lending; Section 2.1. Introduction to Loans; Learning Objectives

• Introduction.- A First Glance at Fourier Method.- Estimation of Integrated Volatility.- Estimation of Instantaneous Volatility.- High Frequency Analysis: Market Microstructure Noise Issues.- Getting Inside the Latent Volatility.- Mathematical Essentials.- Codes for the Fourier Estimator.
• (source: Nielsen Book Data)

This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study.
(source: Nielsen Book Data)

• Interest, Coupons and Yields
• Financial Products
• The No-Arbitrage Principle
• European and American Options
• The Binomial Option Pricing Model
• The Black-Scholes Model
• The Black-Scholes Formula
• Stock-Price Models
• Interest Rate Models
• Numerical Methods
• Simulation Methods
• Calibrating Models -- Inverse Problems
• Case Studies: Exotic Derivatives
• Portfolio Optimization
• Introduction to Credit Risk Models.

Swaps, futures, options, structured instruments - a wide range of derivative products is traded in today's financial markets. Analyzing, pricing and managing such products often requires fairly sophisticated quantitative tools and methods. This book serves as an introduction to financial mathematics with special emphasis on aspects relevant in practice. In addition to numerous illustrative examples, algorithmic implementations are demonstrated using "Mathematica" and the software package "UnRisk" (available for both students and teachers). The content is organized in 15 chapters that can be treated as independent modules. In particular, the exposition is tailored for classroom use in a Bachelor or Master program course, as well as for practitioners who wish to further strengthen their quantitative background.
(source: Nielsen Book Data)

• Generalidades y conceptos
• Interés simple e interés compuesto
• Descuentos y vencimientos
• Tasa de interés nómina y efectiva
• Anualidades
• Sistema de financiación upac, uvr
• Sistemas de amortización
• Métodos para evaluar alternativas
• Títulos valores. .

• Table of Contents:* Money and markets * Fair games * Set theory * Measurable functions * Probability spaces * Expected values * Continuity and integrability * Conditional expectation * Lebesgue measure * Martingales * The Black-Scholes formula * Stochastic integration * Solutions * Bibliography * Index.
• (source: Nielsen Book Data)

The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of this book is to introduce advanced undergraduates and beginning graduate students studying the mathematics of finance to the Black-Scholes formula. The author uses a first-principles approach, developing only the minimum background necessary to justify mathematical concepts and placing mathematical developments in context. The book skillfully draws the reader toward the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It rigorously reveals the mathematical secrets of topics such as abstract measure theory, conditional expectations, martingales, Wiener processes, the Ito calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the universe of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results. The second edition contains numerous revisions and additional material designed to enhance the book's usability as a classroom text. These changes include insights gleaned by the author after teaching from the text, as well as comments and suggestions made by others who used the book. Whereas the revised edition maintains the original approach, format, and list of topics, most chapters are modified to some extent; in addition, the rearrangement of material resulted in a new chapter (Chapter 9). With the modest prerequisite of a first course in calculus, the book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.
(source: Nielsen Book Data)

• Surds
• Indices and logarithm
• Quadratic equation
• Complex numbers
• Set, relation and function
• Profit-loss, discount, commision and brokerage
• Simple interest, average due dates and rebate on bills discounted
• Compound interest and depreciation
• Annuity
• Limit and continuity
• Differential calculus
• Integral calculus (indefinite and definite integration)
• Applications of calculus (application of derivate)
• Point
• Straight line
• Staight lines
• Circle
• Parabola
• Ellipse
• Hyperbola
• Determinant
• Matrix algebra
• Permutation and combination
• Binomial expansion
• Principle of mathematical induction
• Sequence and series.

Whether you need to understand other people#x92; s calculations to make confident business decisions, or formulate investment choices based on your own numbers, this book will give you the tools you need. Banks and financial institutions, businesses and politicians often spin their statistics as they know they can rely on customers or constituents not to understand or check maths and formulas. This book introduces you to the basic tools of maths, statistics and business calculations so that that you can understand the numbers, work out your own calculations and make better investing, saving and business decisions.

• Money and markets Fair games Set theory Measurable functions Probability spaces Expected values Continuity and integrability Conditional expectation Martingales The Black-Scholes formula Stochastic integration Solutions Bibliography Index.
• (source: Nielsen Book Data)

The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of this book is to introduce advanced undergraduates and beginning graduate students studying the mathematics of finance to the Black-Scholes formula. The author uses a first-principles approach, developing only the minimum background necessary to justify mathematical concepts and placing mathematical developments in context.The book skillfully draws the reader toward the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It rigorously reveals the mathematical secrets of topics such as abstract measure theory, conditional expectations, martingales, Wiener processes, the Ito calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the universe of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results. With the modest prerequisite of a first course in calculus, the book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.
(source: Nielsen Book Data)

• About the Author-- Preface--
• 1. Introduction--
• 2. Asset Utilization Measurements-- Sales to Working Capital Ratio-- Sales to Fixed Assets Ratio-- Sales to Administrative Expenses Ratio-- Sales to Equity Ratio-- Sales per Person-- Sales Backlog Ratio-- Sales Returns to Gross Sales Ratio-- Repairs and Maintenance Expense to Fixed Assets Ratio-- Accumulated Depreciation to Fixed Assets Ratio-- Fringe Benefits to Wages and Salaries Expense-- Sales Expenses to Sales Ratio-- Discretionary Cost Ratio-- Interest Expense to Debt Ratio-- Foreign Exchange Ratios-- Overhead Rate-- Goodwill to Assets Ratio-- Overhead to Cost of Sales Ratio-- Investment Turnover-- Break-Even Point-- Margin of Safety-- Tax Rate Percentage--
• 3. Operating Performance Measurements-- Operating Assets Ratio-- Sales to Operating Income Ratio-- Sales Margin-- Gross Profit Percentage-- Gross Profit Index-- Investment Income Percentage-- Operating Profit Percentage-- Operating Leverage Ratio-- Net Income Percentage-- Profit per Person--
• 4. Cash Flow Measurements-- Cash Flow from Operations-- Cash Flow Return on Sales-- Fixed Charge Coverage-- Expense Coverage Days-- Cash Flow Coverage Ratio-- Cash Receipts to Billed Sales and Progress Payments-- Cash to Current Assets Ratio-- Cash Flow to Fixed Asset Requirements-- Cash Flow Return on Assets-- Cash to Working Capital Ratio-- Cash Reinvestment Ratio-- Cash to Current Liabilities Ratio-- Cash Flow to Debt Ratio-- Stock Price to Cash Flow Ratio-- Dividend Payout Ratio--
• 5. Liquidity Measurements-- Accounts Receivable Turnover-- Average Receivable Collection Period-- Days Delinquent Sales Outstanding-- Days Sales in Receivables Index-- Accounts Receivable Investment-- Ending Receivable Balance-- Inventory to Sales Ratio-- Inventory Turnover-- Inventory to Working Capital Ratio-- Liquidity Index-- Accounts Payable Days-- Accounts Payable Turnover-- Current Ratio-- Quick Ratio-- Cash Ratio-- Sales to Current Assets Ratio-- Working Capital Productivity-- Defensive Interval Ratio-- Current Liability Ratio-- Required Current Liabilities to Total Current Liabilities Ratio-- Working Capital to Debt Ratio-- Risky Asset Conversion Ratio-- Noncurrent Assets to Noncurrent Liabilities Ratio-- Short-term Debt to Long-term Debt Ratio-- Altman's Z-Score Bankruptcy Prediction Formula--
• 6. Capital Structure and Solvency Measurements-- Times Interest Earned-- Debt Coverage Ratio-- Asset Quality Index-- Accruals to Assets Ratio-- Times Preferred Dividend Earned-- Debt to Equity Ratio-- Funded Capital Ratio-- Retained Earnings to Stockholders' Equity-- Preferred Stock to Total Stockholders' Equity-- Issued Shares to Authorized Shares--
• 7. Return on Investment Measurements-- Net Worth-- Book Value Per Share-- Tangible Book Value-- Return on Assets Employed-- Return on Operating Assets-- Return on Equity Percentage-- Return on Common Equity-- Financial Leverage Index-- Equity Growth Rate-- Earnings per Share-- Percentage Change in Earnings Per Share-- Economic Value Added-- Dividend Payout Ratio-- Dividend Yield Ratio--
• 8. Market Performance Measurements-- Insider Stock Buy-Sell Ratio-- Market Value Added-- Stock Options to Common Shares Ratio-- Cost of Capital-- Sales to Stock Price Ratio-- Price/Earnings Ratio-- Capitalization Rate--
• 9. Measurements for the Accounting/Finance Department-- Purchase Discounts Taken to Total Discounts-- Percentage of Payment Discounts Missed-- Transactions Processed per Person-- Transaction Error Rate-- Average Time to Issue Invoices-- Average Employee Expense Report Turnaround Time-- Payroll Transaction Fees per Employee-- Time to Produce Financial Statements-- Percentage of Tax Filing Dates Missed-- Proportion of Products Costed Prior to Release-- Internal Audit Savings to Cost Percentage-- Internal Audit Efficiency-- Bad Debt Percentage-- Percent of Receivables over XX Days Old-- Percentage Collected of Dollar Volume Assigned-- Percent of Cash Applied on Day of Receipt-- Cost of Credit-- Earnings Rate on Invested Funds-- Brokerage Fee Percentage-- Borrowing Base Usage Percentage--
• 10. Measurements for the Engineering Department-- Bill of Material Accuracy-- Labor Routing Accuracy-- Percentage of New Products Introduced-- Percentage of Sales from New Products-- Percentage of New Parts Used in New Products-- Percentage of Existing Parts Reused in New Products-- Average Number of Distinct Products per Design Platform-- Percentage of Products Reaching Market before Competition-- Ratio of Actual to Target Cost-- Warranty Claims Percentage-- Time from Design Inception to Production-- Percentage of Floor Space Utilization--
• 11. Measurements for the Logistics Department-- Production Schedule Accuracy-- Economic Order Quantity-- Number of Orders to Place in a Period-- Economic Production Run Size-- Raw Material Inventory Turns-- Raw Material Content-- Finished Goods Inventory Turns-- Obsolete Inventory Percentage-- Percentage of Inventory XX Days Old-- Percentage of Returnable Inventory-- Inventory Accuracy-- Percentage of Certified Suppliers-- Electronic Data Interchange Supplier Percentage-- On-Time Parts Delivery Percentage-- Purchased Component Defect Rate-- Incoming Components Correct Quantity Percentage-- Percentage of Actual Payments Varying from Purchase Order Price-- Percentage of Purchase Orders Issued below Minimum Dollar Level-- Proportion of Corporate Credit Card Usage-- Percentage of Receipts Authorized by Purchase Orders-- Freight Audit Recovery Ratio-- Picking Accuracy for Assembled Products-- Average Time to Ship-- On-Time Delivery Percentage-- Percentage of Products Damaged in Transit-- Percentage of Sales through Distributors--
• 12. Measurements for the Production Department-- Constraint Productivity-- Constraint Rework Percentage-- Constraint Schedule Attainment-- Constraint Utilization-- Degree of Unbalance-- Throughput Effectiveness-- Break-Even Plant Capacity-- Manufacturing Effectiveness-- Productivity Index-- Unit Output per Direct Labor Hour-- Average Equipment Setup Time-- Unscheduled Machine Downtime Percentage-- Acceptable Product Completion Percentage-- Work-in-Process Turnover-- Scrap Percentage-- Warranty Claims Percentage-- Maintenance Expense to Fixed Assets Ratio-- Indirect Expense Index-- Reorder Point-- On-Time Delivery Ratio--
• 13. Measurements for the Sales and Marketing Department-- Market Share-- Customer Turnover-- Browse to Buy Conversion Ratio-- Recency-- Direct Mail Effectiveness Ratio-- Inbound Telemarketing Retention Ratio-- Quote to Close Ratio-- Sales per Salesperson-- Sales Productivity-- Sales Effectiveness-- Sales Trend Percentage by Product Line-- Product Demand Elasticity-- Days of Backlog--
• 14. Measurement Analysis with an Electronic Spreadsheet-- Financial Statement Proportional Analysis-- Financial Statement Ratio Analysis-- Automated Ratio Result Analysis-- Leverage Analysis-- Trend Analysis-- Forecasting-- Cash Flow Analysis-- Capital Asset Analysis-- Compounding Analysis-- Investment Analysis-- Risk Analysis-- Glossary-- Appendix: Measurement Summary-- Index.
• (source: Nielsen Book Data)

A complete appraisal of analytical tools available to managers to assess performance "Steve Bragg has created a useful, relevant guide to applying performance measurements across the organization. His practical explanations and examples should enable managers to apply sophisticated performance measures in a straightforward manner. This book will be a great tool for process improvement. It should be well received by managers, accountants, and consultants." -Clint Davies, Partner (Principal) Berry, Dunn, McNeil & Parker Business managers require a variety of analytical tools to assess a host of organizational performance standards-from finance, efficiency, capacity, and market share to asset utilization, cash flows, liquidity, and capital structure. Steven Bragg's Business Ratios and Formulas represents a comprehensive resource of nearly 200 operational criteria, allowing managers and auditors to pick and choose the tools they need to best assess their organization's performance. Each cataloged measurement includes a description, an example, and some time-tested troubleshooting. Business Ratios and Formulas proves an authoritative resource for managers wishing to thoroughly assess organizational performance.
(source: Nielsen Book Data)

• MAKING DECISIONS WITH TIME VALUE OF MONEY: IT MAKES CENTS. The Basics of Time Value of Money. The Dynamics of Compounding. The Significance of Present Value. The Fundamentals of Cash Flows. The Beauty of Bonds. The Decision-Making Power of Internal Rate of Return and Net Present Value. BUSINESS STATISTICS: MAKING DECISIONS FROM DATA. Organizing Your Data for Better Decision Making. Describing Variation. Fundamentals of Probability Distributions. Probability and the Normal Distribution. Hypothesis Testing. Regression and Estimation. ALL THE ALGEBRA AND HIGH SCHOOL MATH YOU NEED FOR BUSINESS. Algebra Redux. Appendix. Index.
• (source: Nielsen Book Data)

The Fast Forward MBA in Business Math brings you the information you need when you need it most-now! This practical, easy-to-use guide gives you instant access to such crucial business math concepts as algebra, time value of money, and statistics. In short, lively segments using real-world examples, Professor Peter Garrity of Columbia Business School delivers the facts you need to master everyday business math problems-whether in product development, forecasting budgets, or even starting a business. You'll find brief descriptions of key business math concepts, tips on real-world applications, compact case studies, and technology shortcuts. Here are all the tools you need to manage even the most intricate business math problems. You'll discover: How to master the basic quantitative skills that are part of any business environment, such as future and present value, internal rate of return, and net present value Tips for using the latest software and technology tools to solve business math problems How to use statistics for decision making, such as descriptive statistical analysis and regression And much more From the creators of the bestselling Portable MBA series comes The Fast Forward MBA ...A quick way to brush up on new ideas An easy-to-use format that fits in any briefcase Real-world information that you can put to use now!.
(source: Nielsen Book Data)

• Contents: B. Biais, J.C. Rochet: Risk sharing, adverse selection and market structure.- T. Bjork: Interest rate theory.- J. Cvitanic: Optimal trading under constraints.- N. El Karoui, M.C. Quenez: Nonlinear pricing theory and backward stochastic differential equations.- E. Jouini: Market imperfections, equilibrium and arbitrage.
• (source: Nielsen Book Data)

Financial Mathematics is an exciting, emerging field of application. The five sets of course notes in this book provide a bird's eye view of the current "state of the art" and directions of research. For graduate students it will therefore serve as an introduction to the field while reseachers will find it a compact source of reference. The reader is expected to have a good knowledge of the basic mathematical tools corresponding to an introductory graduate level and sufficient familiarity with probabilistic methods, in particular stochastic analysis.
(source: Nielsen Book Data)

In this text, the author discusses the main aspects of mathematical finance. These include, arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last 15 years due to the methodologies of stochastic analysis and control. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.
(source: Nielsen Book Data)