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Stochastic Calculus for Finance I
  • Language: en
  • Pages: 212

Stochastic Calculus for Finance I

Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

Brownian Motion and Stochastic Calculus
  • Language: en
  • Pages: 490

Brownian Motion and Stochastic Calculus

  • Type: Book
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  • Published: 2014-03-27
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  • Publisher: Springer

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

Stochastic Calculus for Finance II
  • Language: en
  • Pages: 586

Stochastic Calculus for Finance II

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Methods of Mathematical Finance
  • Language: en
  • Pages: 427

Methods of Mathematical Finance

This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion- driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treate...

Stochastic Calculus for Finance II
  • Language: en

Stochastic Calculus for Finance II

  • Type: Book
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  • Published: 2010-12-01
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  • Publisher: Springer

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Mathematical Finance
  • Language: en
  • Pages: 161

Mathematical Finance

Now a vital part of modern economies, the rapid growth of the finance industry in recent decades is largely due to the development of mathematical methods such as the theory of arbitrage. Asset valuation, credit trading, and fund management, now depend on these mathematical tools. Mark Davis explains the theories and their applications.

Methods of Mathematical Finance
  • Language: en
  • Pages: 415

Methods of Mathematical Finance

  • Type: Book
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  • Published: 2017-01-10
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  • Publisher: Springer

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Financial Calculus
  • Language: en
  • Pages: 252

Financial Calculus

A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

Stochastic Optimal Control
  • Language: en
  • Pages: 323

Stochastic Optimal Control

  • Type: Book
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  • Published: 1961
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  • Publisher: Unknown

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Stochastic Calculus for Finance II
  • Language: en
  • Pages: 550

Stochastic Calculus for Finance II

  • Type: Book
  • -
  • Published: 2010-12-01
  • -
  • Publisher: Springer

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM