Author | Elliott, Robert J. author |
---|---|

Title | Mathematics of Financial Markets [electronic resource] / by Robert J. Elliott, P. Ekkehard Kopp |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-7146-6 |

Descript | XI, 292 p. online resource |

SUMMARY

This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and prob ability. The emphasis throughout is on developing the mathematical concepts reยญ quired for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or 'exotic') financial instruยญ ments that now appear on the derivatives markets; the focus throughout remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to financial markets. The first five chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by nonarbitrage) is presented in Chapter 1. The unique price for a European option in a singleยญ period binomial model is given and then extended to multi-period binomial models. Chapter 2 intro duces the idea of a martingale measure for price proยญ cesses. Following a discussion of the use of self-financing trading strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price process is a marยญ tingale

CONTENT

1 Pricing by Arbitrage -- 2 Martingale Measures -- 3 The Fundamental Theorem of Asset Pricing -- 4 Complete Markets and Martingale Representation -- 5 Stopping Times and American Options -- 6 A Review of Continuous-Time Stochastic Calculus -- 7 European Options in Continuous Time -- 8 The American Option -- 9 Bonds and Term Structure -- 10 Consumption-Investment Strategies -- References

Mathematics
Economics Mathematical
Probabilities
Statistics
Mathematics
Quantitative Finance
Probability Theory and Stochastic Processes
Statistics general