Mathematical Finance, Introduction to Continuous Time Financial Market Models

Author: Christian-Oliver Ewald
Type: Study Notes, Lecture Notes, e-book
Level: Advanced MBA, MSc(Math. Fin, Fin) , Ph.D.(Fin)

These lecture notes by Christian-Oliver Ewald are a short introduction to mathematical finance. MBA students and non-math major graduates will benefit from these notes. Chapter 1 deals with stochastic processes in continuous time. In chapter 2 the reader can find many topics about financial market theory such as arbitrage, martingale measures, hedging, completeness and pricing of options. Stochastic integration is covered in chapter 3. You can read about stochastic integrals, quadratic variation, Itō's lemma and Girsanov theorem. In chapter 4 the author covers the topics of the generalized Black Scholes model, the stochastic volatility model and the Poisoon market model. Finally, chapter 5 deals with portfolio optimization in continuous time both using the martingale and the stochastic control approaches.

Download Christian-Oliver Ewald's "Mathematical Finance, Introduction to Continuous Time Financial Market Models" using the link below

Stochastic Calculus, Filtering, and Stochastic Control

Author: Ramon van Handel
Type: Study Notes, Lecture Notes, e-book
Level: MSc(Math. Fin), Ph.D.(Fin)

These lecture notes for the course "Stochastic Calculus and Stochastic Control" from Ramon van Handel are an excellent coverage of the topic. The notes are very intuitive and thus are appropriate for readers with major other than mathematics. The lecture notes provide the necessary background, probability theory, stochastic processes, martingales, the wiener process (Brownian motion). Stochastic integrals, Itō's lemma and stochastic differential equatios (SDEs) are covered in later chapters. After the necessary background, optimal control and filtering theory are covered next. Optimal stopping is discussed in the final chapter.

You can download Ramon van Handel's "Stochastic Calculus, Filtering, and Stochastic Control" using the following link

Financial Mathematics I, Stochastic Calculus, Option Pricing, Portfolio Optimization

Author: Holger Kraft
Type: Study Notes, Lecture Notes
Type: Advanced Undregraduate(Math), MSc(Math. Fin), Ph.D.(Fin)

The lecture notes "Financial Mathematics I, Stochastic Calculus, Option Pricing, Portfolio Optimization" cover the topics of discrete-time pricing, stochastic calculus and continuous-time pricing and portfolio optimization. In chapter 2, both single-period and multi-period models are considered. The reader can find information about Arrow-Debreu securities and risk neutral measures. An introduction to stochastic calculus is provided in chapter 3. Stochastic processes, martingales, Itō integrals and Itō's lemma are discussed. In chapter 4, the topic of option pricing in continuous-time is discussed. The topic of chapter 5 is the continuous-time portfolio problem, and both the martingale approach and the stochastic optimal control approach are discussed.

Download Holger Kraft's "Financial Mathematics I, Stochastic Calculus, Option Pricing, Portfolio Optimization" using the link that follows