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Stochastic finance and financial engineering have been rapidlyexpanding fields of science over the past four decades, mainly dueto the success of sophisticated quantitative methodologies inhelping professionals manage financial risks. In recent years, wehave witnessed a tremendous acceleration in research efforts aimedat better comprehending, modeling and hedging this kind ofrisk. These two volumes aim to provide a foundation course on appliedstochastic finance. They are designed for three groups of readers:firstly, students of various backgrounds seeking a core knowledgeon the subject of stochastic finance; secondly financial analystsand practitioners in the investment, banking and insuranceindustries; and finally other professionals who are interested inlearning advanced mathematical and stochastic methods, which arebasic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financialinstruments and the fundamental principles of financial modelingand arbitrage valuation of derivatives. Next, we use thediscrete-time binomial model to introduce all relevant concepts.The mathematical simplicity of the binomial model also provides uswith the opportunity to introduce and discuss in depth conceptssuch as conditional expectations and martingales in discrete time.However, we do not expand beyond the needs of the stochasticfinance framework. Numerous examples, each highlighted and isolatedfrom the text for easy reference and identification, areincluded. The book concludes with the use of the binomial model tointroduce interest rate models and the use of the Markov chainmodel to introduce credit risk. This volume is designed in such away that, among other uses, makes it useful as an undergraduatecourse.