TY  - BOOK
AU  - Epps,T.W.
TI  - Quantitative finance: its development, mathematical foundations, and current scope 
SN  - 0470431997
AV  - HG106 .E67 2009
U1  - 332.015195 22
PY  - 2009///]
CY  - Hoboken, N.J.
PB  - Wiley
KW  - Finance
KW  - Mathematical models
KW  - Investments
N1  - Includes bibliographical references (pages 391-395) and index; Part I; Perspective and Preparation --; 1; Introduction and Overview --; 1.1; An Elemental View of Assets and Markets --; 1.1.1; Assets as Bundles of Claims --; 1.1.2; Financial Markets as Transportation Agents --; 1.1.3; Why Is Transportation Desirable? --; 1.1.4; What Vehicles Are Available? --; 1.1.5; What Is There to Learn about Assets and Markets? --; 1.1.6; Why the Need for Quantitative Finance? --; 1.2; Where We Go from Here --; 2; Tools from Calculus and Analysis --; 2.1; Some Basics from Calculus --; 2.2; Elements of Measure Theory --; 2.2.1; Sets and Collections of Sets --; 2.2.2; Set Functions and Measures --; 2.3; Integration --; 2.3.1; Riemann-Stieltjes --; 2.3.2; Lebesgue /Lebesgue-Stieltjes --; 2.3.3; Properties of the Integral --; 2.4; Changes of Measure --; 3; Probability --; 3.1; Probability Spaces --; 3.2; Random Variables and Their Distributions --; 3.3; Independence of R.V.s --; 3.4; Expectation --; 3.4.1; Moments --; 3.4.2; Conditional Expectations and Moments --; 3.4.3; Generating Functions --; 3.5; Changes of Probability Measure --; 3.6; Convergence Concepts --; 3.7; Laws of Large Numbers and Central Limit Theorems --; 3.8; Important Models for Distributions --; 3.8.1; Continuous Models --; 3.8.2; Discrete Models --; Part II; Portfolios and Prices --; 4; Interest and Bond Prices --; 4.1; Interest Rates and Compounding --; 4.2; Bond Prices, Yields, and Spot Rates --; 4.3; Forward Bond Prices and Rates --; 4.4; Empirical Project #1 --; 5; Models of Portfolio Choice --; 5.1; Models That Ignore Risk --; 5.2; Mean-Variance Portfolio Theory --; 5.2.1; Mean-Variance 'Efficient' Portfolios --; 5.2.2; The Single-Index Model --; 5.3; Empirical Project #2 --; 6; Prices in a Mean-VarianceWorld --; 6.1; The Assumptions --; 6.2; The Derivation --; 6.3; Interpretation --; 6.4; Empirical Evidence --; 6.5; Some Reflections --; 7; Rational Decisions under Risk --; 7.1; The Setting and the Axioms --; 7.2; The Expected-Utility Theorem --; 7.3; Applying Expected-Utility Theory --; 7.3.1; Implementing EU Theory in Financial Modeling --; 7.3.2; Inferring Utilities and Beliefs --; 7.3.3; Qualitative Properties of Utility Functions --; 7.3.4; Measures of Risk Aversion --; 7.3.5; Examples of Utility Functions --; 7.3.6; Some Qualitative Implications of the EU Model --; 7.3.7; Stochastic Dominance --; 7.4; Is the Markowitz Investor Rational? --; 7.5; Empirical Project #3 --; 8; Observed Decisions under Risk --; 8.1; Evidence about Choices under Risk --; 8.1.1; Allais? Paradox --; 8.1.2; Prospect Theory --; 8.1.3; Preference Reversals --; 8.1.4; Risk Aversion and Diminishing Marginal Utility --; 8.2; Toward 'Behavioral' Finance --; 9; Distributions of Returns --; 9.1; Some Background --; 9.2; The Normal /Lognormal Model --; 9.3; The Stable Model --; 9.4; Mixture Models --; 9.5; Comparison and Evaluation --; 10; Dynamics of Prices and Returns --; 10.1; Evidence for First-Moment Independence --; 10.2; Random Walks and Martingales --; 10.3; Modeling Prices in Continuous Time --; 10.3.1; Poisson and Compound-Poisson Processes --; 10.3.2; Brownian Motions --; 10.3.3; Martingales in Continuous Time --; 10.4; Empirical Project #4 --; 11; Stochastic Calculus --; 11.1; Stochastic Integrals --; 11.1.1; Ito Integrals with Respect to a B.m --; 11.1.2; From It^o Integrals to It^o Processes --; 11.1.3; Quadratic-Variations of It^o Processes --; 11.1.4; Integrals with Respect to It^o Processes --; 11.2; Stochastic Differentials --; 11.3; Ito's Formula for Differentials --; 11.3.1; Functions of a B.m. Alone --; 11.3.2; Functions of Time and a B.m --; 11.3.3; Functions of Time and General It^o Processes --; 12; Portfolio Decisions over Time --; 12.1; The Consumption-Investment Problem --; 12.2; Dynamic Portfolio Decisions --; 12.2.1; Optimizing via Dynamic Programming --; 12.2.2; A Formulation with Additively-Separable Utility --; 13; Optimal Growth --; 13.1; Optimal Growth in Discrete Time --; 13.2; Optimal Growth in Continuous Time --; 13.3; Some Qualifications --; 13.4; Empirical Project #5 --; 14; Dynamic Models for Prices --; 14.1; Dynamic Optimization (Again) --; 14.2; Static Implications: The CAPM --; 14.3; Dynamic Implications: The Lucas Model --; 14.4; Assessment --; 14.4.1; The Puzzles --; 14.4.2; The Patches --; 14.4.3; Some Reflections --; 15; Efficient Markets --; 15.1; Event Studies --; 15.1.1; Methods --; 15.1.2; A Sample Study --; 15.2; Dynamic Tests --; 15.2.1; Early History --; 15.2.2; Implications of the Dynamic Models --; 15.2.3; Excess Volatility --; Part III; Paradigms for Pricing --; 16; Static Arbitrage Pricing --; 16.1; Pricing Paradigms: Optimization vs. Arbitrage --; 16.2; The APT --; 16.3; Arbitraging Bonds --; 16.4; Pricing a Simple Derivative Asset --; 17; Dynamic Arbitrage Pricing --; 17.1; Dynamic Replication --; 17.2; Modeling Prices of the Assets --; 17.3; The Fundamental P.D.E --; 17.3.1; The Feynman-Kac Solution to the P.D.E --; 17.3.2; Working out the Expectation --; 17.4; Allowing Dividends and Time-Varying Rates --; 18; Properties of Option Prices --; 18.1; Bounds on Prices of European Options --; 18.2; Properties of Black-Scholes Prices --; 18.3; Delta Hedging --; 18.4; Does Black-Scholes StillWork? --; 18.5; American-Style Options --; 18.6; Empirical Project #6 --; 19; Martingale Pricing --; 19.1; Some Preparation --; 19.2; Fundamental Theorem of Asset Pricing --; 19.3; Implications for Pricing Derivatives --; 19.4; Applications --; 19.5; Martingale vs. Equilibrium Pricing --; 19.6; Numeraires, Short Rates, and E.M.M.s --; 19.7; Replication & Uniqueness of the E.M.M --; 20; Modeling Volatility --; 20.1; Models with Price-Dependent Volatility --; 20.1.1; The C.E.V. Model --; 20.1.2; The Hobson-Rogers Model --; 20.2; ARCH /GARCH Models --; 20.3; Stochastic Volatility --; 20.4; Is Replication Possible? --; 21; Discontinuous Price Processes --; 21.1; Merton's Jump-Diffusion Model --; 21.2; The Variance-Gamma Model --; 21.3; Stock Prices as Branching Processes --; 21.4; Is Replication Possible? --; 22; Options on Jump Processes --; 22.1; Options under Jump-Diffusions --; 22.2; A Primer on Characteristic Functions --; 22.3; Using Fourier Methods to Price Options --; 22.4; Applications to Jump Models --; 23; Options on S.V. Processes --; 23.1; Independent Price /Volatility Shocks --; 23.2; Dependent Price /Volatility Shocks --; 23.3; Adding Jumps to the S.V. Model --; 23.4; Further Advances --; 23.5; Empirical Project #7
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