Probability and Finance Theory
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|Format: ||Hardback, 300 pages|
|Published In: ||Singapore, 20 August 2011|
This book provides a basic grounding in the use of probability to model random financial phenomena of uncertainty, and is targeted at an advanced undergraduate and graduate level. It should appeal to finance students looking for a firm theoretical guide to the deep end of derivatives and investments. Bankers and finance professionals in the fields of investments, derivatives, and risk management should also find the book useful in bringing probability and finance together. The book contains applications of both discrete time theory and continuous time mathematics, and is extensive in scope. Distribution theory, conditional probability, and conditional expectation are covered comprehensively, and applications to modeling state space securities under market equilibrium are made. Martingale is studied, leading to consideration of equivalent martingale measures, fundamental theorems of asset pricing, change of numeraire and discounting, risk-adjusted and forward-neutral measures, minimal and maximal prices of contingent claims, Markovian models, and the existence of martingale measures preserving the Markov property. Discrete stochastic calculus and multiperiod models leading to no-arbitrage pricing of contingent claims are also to be found in this book, as well as the theory of Markov Chains and appropriate applications in credit modeling. Measure-theoretic probability, moments, characteristic functions, inequalities, and central limit theorems are examined. The theory of risk aversion and utility, and ideas of risk premia are considered. Other application topics include optimal consumption and investment problems and interest rate theory.
Table of Contents
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"
World Scientific Publishing Co Pte Ltd|
22.86 x 15.75 x 2.54 centimetres (0.70 kg)|
15+ years |