Measure-Theoretic Probability; Moments; Characteristic Functions; Inequalities; Central Limit Theorem; Distribution Theory; Conditional Probability; Conditional Expectation; State Space Securities; Market Equilibrium; Martingales; Equivalent Martingale Measures; Fundamental Theorems of Asset Pricing; Change of Numeraire; Risk-Adjusted and Forward-Neutral Measures; Minimal and Maximal Prices of Contingent Claims; Markovian Models; Stochastic Calculus; No-Arbitrage Pricing of Contingent Claims; Utility Theory; Theory of Risk Aversion; Risk Premia; Theory of Markov Chains; Credit Modeling; Optimal Consumption and Investment; Multi-Period Models; Interest Rate Theory.
This text develops the core ideas of finance in the last 40 years and their applications in an accessible manner without sacrificing rigor. I recommend the texts for scholars teaching financial theory, capital markets, and financial engineering. -- Suresh M Sundaresan "Chase Manhattan Bank Professor of Economics & Finance, Columbia Business School, University of Columbia" This book goes beyond many others on similar topics, presenting the connection between probability and topics in the foundations of modern finance, including derivatives, asset pricing, welfare economics and microeconomic marginal analyses. The exercises scattered throughout the book guide the student along the way on the key ideas and methods discussed. This will also be an important companion to any practitioner working in the area of quantitative finance. -- Chong Chi Tat "University Professor, Department of Mathematics, National University of Singapore"