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正版 随机金融引论 严加安[著] 科学出版社 9787030581440 书籍
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1 Foundation of Probability Theory and Discrete-Time Martingales
1.1 Basic Concepts of Probability Theory
1.1.1 Events and Probability
1.1.2 Independence, 0-1 Law, and Borel-Cantelli Lemma
1.1.3 Integrals, (Mathematical) Expectations of Random Variables
1.1.4 Convergence Theorems
1.2 Conditional Mathematical Expectation
1.2.1 Definition and Basic Properties
1.2.2 Convergence Theorems
1.2.3 Two Theorems About Conditional Expectation
1.3 Duals of Spaces L∞(Ω, F) and L∞(Ω, F, m)
1.4 Family of Uniformly Integrable Random Variables
1.5 Discrete Time Martingales
1.5.1 Basic Definitions
1.5.2 Basic Theorems
1.5.3 Martingale Transforms
1.5.4 Snell Envelop
1.6 Markoy Sequences
2 Portfolio Selection Theory in Discrete.Time
2.1 Mean-Variance Analysis
2.1.1 Mean-Variance Frontier Portfolios Without Risk-Free Asset
2.1.2 Revised Formulations of Mean-Variance Analysis Without Risk-Free Asset
2.1.3 Mean-Variance Frontier Portfolios with Risk-Free Asset
2.1.4 Mean-Variance Utility Functions
2.2 Capital Asset Pricing Model (CAPM)
2.2.1 Market Competitive Equilibrium and Market Portfolio.,
2.2.2 CAPM with Risk-Free Asset
2.2.3 CAPM Without Risk-Free Asset
2.2.4 Equilibrium Pricing Using CAPM
2.3 Arbitrage Pricing Theory (APT)
2.4 Mean-Sernivariance Model
2.5 Multistage Mean-Variance Model
2.6 Expected Utility Theory
2.6.1 Utility Functions
2.6.2 Arrow-Pratt's Risk Aversion Functions
2.6.3 Comparison of Risk Aversion Functions
2.6.4 Preference Defined by Stochastic Orders
2.6.5 Maximization of Expected Utility and Initial Price of Risky Asset
2.7 Consumption-Based Asset Pricing Models
3 Financial Markets in Discrete Time
3.1 Basic Concepts of Financial Markets
3.1.1 Numeraire
3.1.2 Pricing and Hedging
3.1.3 Put-Call Parity
3.1.4 Intrinsic Value and Time Value
3.1.5 Bid-Ask Spread
3.1.6 Efficient Market Hypothesis
3.2 Binomial Tree Model
3.2.1 The One-Period Case
3.2.2 The Multistage Case
本书由浅入深、全面系统地介绍金融数学基本理论,着重介绍鞅方法在未定权益定价和对冲中的应用。内容包含离散时间投资组合选择理论和金融市场模型,Black-Scholes模型及其修正,奇异期权的定价和对冲,It过程和扩散过程模型,利率期限结构模型,最优投资组合与投资-消费策略
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