Stochastic Finance: An Introduction with Examples (Paperback)

Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black-Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.

《隨機金融學》提供了一個在可理解性方面無與倫比的數學金融學入門。通過課堂測試，作者們確定了學生常見的困難點，他們的方法非常謹慎，幫助讀者克服這些困難，並在可比的文本中培養理解能力。本書針對高年級本科生撰寫，並使用大量詳細的例子來說明關鍵概念，提供了在金融世界中建模交易所需的所有數學基礎。唯一需要的背景是概率論的第一門課。本書以離散二項模型和有限市場模型開始，然後介紹連續的Black-Scholes模型。它通過結合金融概念（如套利和自融資交易策略）和概率工具（如sigma代數、鞅和隨機積分）來研究歐式期權的定價。所有這些概念都以輕鬆和用戶友好的方式介紹。