Problems and Solutions in Mathematical Finance 1st Edition by Eric Chin, Sverrir lafsson, Dian Nel – Ebook PDF Instant Download/Delivery: 1119965837 ,9781119965831
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ISBN 10: 1119965837
ISBN 13: 9781119965831
Author: Eric Chin, Sverrir lafsson, Dian Nel
Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance.
Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance.
This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance.
Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.
Problems and Solutions in Mathematical Finance 1st Edition Table of contents:
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Introduction to Mathematical Finance
- Overview of mathematical finance.
- The role of mathematics in financial theory and practice.
- Basic concepts in finance: time value of money, risk, return, and pricing of assets.
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Mathematical Tools for Finance
- Review of essential mathematics: algebra, calculus, probability theory.
- Linear algebra and its applications in finance.
- Probability distributions, expectations, and variances in financial contexts.
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The Time Value of Money
- Present value, future value, and discounting.
- Annuities and perpetuities.
- The time value of money in practical financial decision-making.
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Risk and Return
- Defining risk and return in financial contexts.
- Portfolio theory and diversification.
- Measures of risk: variance, standard deviation, and Value at Risk (VaR).
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Fixed Income Securities
- Pricing bonds and other fixed-income instruments.
- Duration and convexity.
- Yield curves and interest rate modeling.
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Stock Valuation and Pricing Models
- Dividend discount models (DDM) and price/earnings ratios (P/E).
- The Capital Asset Pricing Model (CAPM) and its assumptions.
- Arbitrage pricing theory (APT).
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Options and Derivatives
- Introduction to derivatives: options, futures, swaps, and forwards.
- The Black-Scholes model for option pricing.
- Put-call parity, option Greeks, and hedging strategies.
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Stochastic Processes in Finance
- Random walks and Brownian motion.
- Ito’s Lemma and its applications in pricing options.
- Stochastic differential equations in financial modeling.
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Financial Modelling with Derivatives
- Modelling the behavior of derivative securities.
- Monte Carlo simulations in finance.
- Risk-neutral pricing and hedging.
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Numerical Methods for Financial Problems
- Numerical solutions for pricing options and other derivatives.
- Finite difference methods and binomial trees.
- Simulation techniques in finance.
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Advanced Topics in Mathematical Finance
- Volatility modeling and option pricing under stochastic volatility.
- Credit risk modeling and credit derivatives.
- Exotic options and structured products.
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Case Studies and Real-World Applications
- Case studies of financial crises and risk management failures.
- Applications of mathematical finance in asset management and trading strategies.
- Real-world applications of financial modeling in hedge funds and investment banking.
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Appendices
- Review of mathematical and statistical tools.
- Financial formulas and tables.
- Further readings and references.
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