Optimal Statistical Inference in Financial Engineering (Hardcover)

PREFACE

INTRODUCTION

ELEMENTS OF PROBABILITY
Probability and Probability Distribution
Vector Random Variable and Independence
Expectation and Conditional Distribution
Convergence and Central Limit Theorems

STATISTICAL INFERENCE
Sufficient Statistics
Unbiased Estimators
Efficient Estimators
Asymptotically Efficient Estimators

VARIOUS STATISTICAL METHODS
Interval Estimation
Most Powerful Test
Various Tests
Discriminant Analysis

STOCHASTIC PROCESSES
Elements of Stochastic Processes
Spectral Analysis
Ergodicity, Mixing, and Martingale
Limit Theorems for Stochastic Processes
Exercise

TIME SERIES ANALYSIS
Time Series Model
Estimation of Time Series Models
Model Selection Problems
Nonparametric Estimation
Prediction of Time Series
Regression for Time Series
Long Memory Processes
Local Whittle Likelihood Approach
Nonstationary Processes
Semiparametric Estimation
Discriminant Analysis for Time Series

INTRODUCTION TO STATISTICAL FINANCIAL ENGINEERING
Option Pricing Theory
Higher Order Asymptotic Option Valuation for Non-Gaussian Dependent Returns
Estimation of Portfolio
Value-at-Risk (VaR) Problems

TERM STRUCTURE
Spot Rates and Discount Bonds
Estimation Procedures for Term Structure

CREDIT RATING
Parametric Clustering for Financial Time Series
Nonparametric Clustering for Financial Time Series
Credit Rating Based on Financial Time Series

APPENDIX
REFERENCES
INDEX