The first chapter is the finite-dimensional contingent claim space.

1. 1 finite dimensional linear space

1. 1. 1 finite dimension contingent claim space

1.2 Definition, Subspace, Basis and Dimension of General Linear Space

1.2. 1 For complete markets and incomplete markets with limited dimensions or claim space,

1.3 linear function, linear mapping and its matrix representation

1.3. 1 linear pricing on finite-dimensional contingent claims space

1.3.2 random discount factor in finite-dimensional contingent claim space

1.4 bilinear function

The Bilinear Function in the Portfolio Selection Problem of 1.4. 1

1.5 inner product and Euclidean space

1.5. 1 as the contingent claim space of Euclidean space.

Chapter II Infinite Dimensional Contingency Space

2. 1 infinite dimensional linear space

2. 1. 1 Finance in Infinite Dimensional Linear Space (89)

2.2 convex set and convex set separation theorem

2.2. 1 Basic theorem of asset pricing and convex set separation theorem (97)

2.3 Banach space and its * * * yoke space

2.3. 1 Banactl space and its * * * yoke space in finance (122)

2.4 Hahn-Banactl theorem in normed linear space

2.4. 1 linear pricing in Banach spaces with contingent claims (127)

2.5 Hilbert space and orthogonality

2.5. 1 theory of random discount factor in infinite-dimensional contingent claim space (144)

2.6 Discussion on Some Issues of axiom of choice

Chapter III Financial Optimization

3. 1 convex function and its main properties

3. 1. 1 Function Convexity in Economy and Finance (164)

3.2 Optimization Problems and Kuhn-Luc Conditions

3.2. 1 Mathematical Programming in Portfolio Selection Theory (187)

3.2.2 Optimal allocation of resources and optimal investment-consumption problem (20 1)

Chapter IV Mathematical Description of Financial Information Structure

4. 1 axiomatic system of probability theory

4. 1. 1 Rational Expectation Model of Financial Efficient Market Theory (22 1)

4.2 Random Walk Theory

4.2. 1 Random Walk and Efficient Market Theory (236)

4.2.2 Binary Tree Method Black Scholes Option Pricing Formula (24 1)

4.3 Discrete algebraic flows and martingales

4.3. 1 Multi-period Securities Market Model and Basic Theorem of Asset Pricing in Finite State (257)

4.3.2 Basic Theorem of Asset Pricing in Infinite State (269)

The fifth chapter is the mathematical basis of continuous-time finance.

5. 1 is Brownian motion and walks continuously at random.

5. Original derivation of the formula1.1blaclscholes (293)

5. 1.2 Stochastic Differential Equation of Term Structure of Interest Rate (300)

5.2 Continuous Time Financial Market Model and Basic Theorem of Asset Pricing

refer to

Noun index

postscript