Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authorsa teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.Suppose there are two assets X and Y with initial prices X0 and Y0. ... Consider two investments with respective wealth functions Vt and Wt, with t a [0, T]. ... In the latter case, the discounted stock price process St/Bt is said to be a martingale. ... money market account A. Suppose that the possible stock prices at time t = T are as follows: ST = Su with probability p1 agt; 0, Sm with probability p2 agt; 0, anbsp;...

Title | : | Financial Mathematics |

Author | : | Giuseppe Campolieti, Roman N. Makarov |

Publisher | : | CRC Press - 2014-03-12 |

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