Sale!

Mathematical Techniques in Finance Tools for Incomplete Markets 2nd Edition by Ales Cerný 1400831482 9781400831487

Original price was: $50.00.Current price is: $35.00.

Mathematical Techniques in Finance Tools for Incomplete Markets Second Edition Ales Cerný Digital Instant Download

Author(s): Ales Cerný
ISBN(s): 9781400831487, 1400831482
Edition: Second
File Details: PDF, 2.64 MB
Year: 2009
Language: english
SKU: EB-51946328 Category: Tag:

Mathematical Techniques in Finance Tools for Incomplete Markets 2nd Edition by Ales Cerný – Ebook PDF Instant Download/Delivery: 1400831482, 9781400831487

Full download Mathematical Techniques in Finance Tools for Incomplete Markets 2nd Edition after payment

Product details:

ISBN 10: 1400831482 

ISBN 13: 9781400831487

Author: Ales Cerný

Originally published in 2003, Mathematical Techniques in Finance has become a standard textbook for master’s-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.

The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated.

  • A standard textbook for graduate finance courses
  • Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation
  • Detailed examples and MATLAB codes integrated throughout the text
  • Exercises and summaries of main points conclude each chapter

Table of contents:

1 – The Simplest Model of Financial Markets

1.1 One-Period Finite State Model

1.2 Securities and Their Payoffs

1.3 Securities as Vectors

1.4 Operations on Securities

1.5 The Matrix as a Collection of Securities

1.6 Transposition

1.7 Matrix Multiplication and Portfolios

1.8 Systems of Equations and Hedging

1.9 Linear Independence and Redundant Securities

1.10 The Structure of the Marketed Subspace

1.11 The Identity Matrix and Arrow–Debreu Securities

1.12 Matrix Inverse

1.13 Inverse Matrix and Replicating Portfolios

1.14 Complete Market Hedging Formula

1.15 Summary

1.16 Notes

1.17 Exercises

2 – Arbitrage and Pricing in the One-Period Model

2.1 Hedging with Redundant Securities and Incomplete Market

2.2 Finding the Best Approximate Hedge

2.3 Minimizing the Expected Squared Replication Error

2.4 Numerical Stability of Least Squares

2.5 Asset Prices, Returns and Portfolio Units

2.6 Arbitrage

2.7 No-Arbitrage Pricing

2.8 State Prices and the Arbitrage Theorem

2.9 State Prices and Asset Returns

2.10 Risk-Neutral Probabilities

2.11 State Prices and No-Arbitrage Pricing

2.12 Asset Pricing Duality

2.13 Summary

2.14 Notes

2.15 Appendix: Least Squares with QR Decomposition

2.16 Exercises

3 – Risk and Return in the One-Period Model

3.1 Utility Functions

3.2 Expected Utility Maximization

3.3 The Existence of Optimal Portfolios

3.4 Reporting Expected Utility in Terms of Money

3.5 Normalized Utility and Investment Potential

3.6 Quadratic Utility

3.7 The Sharpe Ratio

3.8 Arbitrage-Adjusted Sharpe Ratio

3.9 The Importance of Arbitrage Adjustment

3.10 Portfolio Choice with Near-Arbitrage Opportunities

3.11 Summary

3.12 Notes

3.13 Exercises

4 – Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets

4.1 Sensitivity Analysis of Portfolio Decisions with the CRRA Utility

4.2 Newton’s Algorithm for Optimal Investment with CRRA Utility

4.3 Optimal CRRA Investment Using Empirical Return Distribution

4.4 HARA Portfolio Optimizer

4.5 HARA Portfolio Optimization with Several Risky Assets

4.6 Quadratic Utility Maximization with Multiple Assets

4.7 Summary

4.8 Notes

4.9 Exercises

5 – Pricing in Dynamically Complete Markets

5.1 Options and Portfolio Insurance

5.2 Option Pricing

5.3 Dynamic Replicating Trading Strategy

5.4 Risk-Neutral Probabilities in a Multi-Period Model

5.5 The Law of Iterated Expectations

5.6 Summary

5.7 Notes

5.8 Exercises

6 – Towards Continuous Time

6.1 IID Returns, and the Term Structure of Volatility

6.2 Towards Brownian Motion

6.3 Towards a Poisson Jump Process

6.4 Central Limit Theorem and Infinitely Divisible Distributions

6.5 Summary

6.6 Notes

6.7 Exercises

7 – Fast Fourier Transform

7.1 Introduction to Complex Numbers and the Fourier Transform

7.2 Discrete Fourier Transform (DFT)

7.3 Fourier Transforms in Finance

7.4 Fast Pricing via the Fast Fourier Transform (FFT)

7.5 Further Applications of FFTs in Finance

7.6 Notes

7.7 Appendix

7.8 Exercises

8 – Information Management

8.1 Information: Too Much of a Good Thing?

8.2 Model-Independent Properties of Conditional Expectation

8.3 Summary

8.4 Notes

8.5 Appendix: Probability Space

8.6 Exercises

9 – Martingales and Change of Measure in Finance

9.1 Discounted Asset Prices Are Martingales

9.2 Dynamic Arbitrage Theorem

9.3 Change of Measure

9.4 Dynamic Optimal Portfolio Selection in a Complete Market

9.5 Summary

9.6 Notes

9.7 Exercises

10 – Brownian Motion and Itô Formulae

10.1 Continuous-Time Brownian Motion

10.2 Stochastic Integration and Itô Processes

10.3 Important Itô Processes

10.4 Function of a Stochastic Process: the Itô Formula

10.5 Applications of the Itô Formula

10.6 Multivariate Itô Formula

10.7 Itô Processes as Martingales

10.8 Appendix: Proof of the Itô Formula

10.9 Summary

10.10 Notes

10.11 Exercises

11 – Continuous-Time Finance

11.1 Summary of Useful Results

11.2 Risk-Neutral Pricing

11.3 The Girsanov Theorem

11.4 Risk-Neutral Pricing and Absence of Arbitrage

11.5 Automatic Generation of PDEs and the Feynman–Kac Formula

11.6 Overview of Numerical Methods

11.7 Summary

11.8 Notes

11.9 Appendix: Decomposition of Asset Returns into Uncorrelated Components

11.10 Exercises

12 – Finite-Difference Methods

12.1 Interpretation of PDEs

12.2 The Explicit Method

12.3 Instability

12.4 Markov Chains and Local Consistency

12.5 Improving Convergence by Richardson’s Extrapolation

12.6 Oscillatory Convergence Due to Grid Positioning

12.7 Fully Implicit Scheme

12.8 Crank–Nicolson Scheme

12.9 Summary

12.10 Notes

12.11 Appendix: Efficient Gaussian Elimination for Tridiagonal Matrices

12.12 Appendix: Richardson’s Extrapolation

12.13 Exercises

13 – Dynamic Option Hedging and Pricing in Incomplete Markets

13.1 The Risk in Option Hedging Strategies

13.2 Incomplete Market Option Price Bounds

13.3 Towards Continuous Time

13.4 Derivation of Optimal Hedging Strategy

13.5 Summary

13.6 Notes

13.7 Appendix: Expected Squared Hedging Error in the Black-Scholes Model

13.8 Exercises

Appendix A – Calculus

A.1 Notation

A.2 Differentiation

A.3 Real Function of Several Real Variables

A.4 Power Series Approximations

A.5 Optimization

A.6 Integration

A.7 Exercises

Appendix B – Probability

B.1 Probability Space

B.2 Conditional Probability

B.3 Marginal and Joint Distribution

B.4 Stochastic Independence

B.5 Expectation Operator

B.6 Properties of Expectation

B.7 Mean and Variance

B.8 Covariance and Correlation

B.9 Continuous Random Variables

B.10 Normal Distribution

B.11 Quantiles

B.12 Relationships among Standard Statistical Distributions

B.13 Notes

B.14 Exercises

People also search:

tools used in finance

mathematical techniques in finance

financial tools and techniques

tools of financial analysis

methods of mathematical finance

Tags: Ales Cerný, Mathematical, Techniques, Finance