Probability and finance theory

1. Probability Distributions 2. Conditional Probability 3. Laws of Probability 4. Theory of Risk and Utility 5. State Price and Risk-Neutral Probability 6. Single Period Asset Pricing Models 7. Stochastic Processes and Martingales 8. Dynamic Programming and Multi-period Asset Pricing 9. Continuous-Time Asset Pricing Model 10. Continuous-Time Option Pricing 11. Hedging and More Option Pricing 12. Brownian Motion and Technical Trading 13. Theory of Markov Chains and Credit Markets 14. Interest Rate Modeling and Derivatives 15. Risk Measures

This book introduces mathematical analysis of probability theory, focusing on its application in finance theory and applications. It provides an integrated overview of both basic probability theory and finance theory, making it useful for advanced undergraduates or first-year postgraduates. The book links applied probability and finance theory, covering key ideas in finance over the last 50 years. It also serves as a guide for applied mathematicians and probabilists to access important topics in finance theory and economics.