吉利编著的《金融中的数值方法和优化》旨在为读者介绍金融计算工具—基本数值分析和计算技巧，如期权定价、并突出了模拟和优化的重要性，用许多章讲述投资组合保险和风险估计问题。特别地，有几章用于讲述优化探索和如何将他们应用于投资组合的选择、估值的校准和期权定价模型。这些具体的例子让读者学习了解决问题的具体步骤，以及将这些步骤举一反三。同时，这些应用使得本书的参考价值大大提高。

list of algorithms

acknowledgements

1. introduction

 1.1 about this book

 1.2 principles

 1.3 on software

 1.4 on approximations and accuracy

 1.5 summary: the theme of the book

 part one fundamentals

2. numerical analysis in a nutshell

 2.1 computer arithmetic

 representation of real numbers

 machine precision

 example of limitations of floating point arithmetic

 2.2 measuring errors

 2.3 approxinaating derivatives with finite differences

 approximating first-order derivatives

 approximating second order derivatives

 partial derivatives

 .how to choose h

 truncation error for forward difference

 2.4 numerical instability and ill-conditioning

 example ora numerically unstable algorithm

 example of an ill-conditioned problem

 2.5 condition number of a matrix

 comments and examples

 2.6 a primer on algorithmic and computational complexity

 2.6.1 criteria for comparison

 order of complexity and classification

 2.a operation count for basic linear algebra operations

3. linear equations and least squares problems

 choice of method

 3. 1 direct methods

 3.1.1 triangular systems

 3.1.2 lu factorization

 3.1.3 cholcsky factorization

 3.1.4 qr decomposition

 3.1.5 singular value decomposition

 3.2 iterative methods

 3.2.1 lacobi, gauss-seidel, and sor

 successive overrelaxation

 3.2.2 convergence of iterative methods

 3.2.3 general structure of algorithms for iterative methods

 3.2.4 block iterative methods

 3.3 sparse linear systems

 3.3.1 tridiagonal systems

 3.3.2 irregular sparse matriccs

 3.3.3 structural properties of sparse matrices

 3.4 the least squares problem

 3.4.1 method of normal equations

 3.4.2 least squares via qr factorization

 3.4.3 l.east squares via svd decomposition

 3.4.4 final remarks

 the backslash operator in matlab

4. finite difference methods

 4.1 an example of a numerical solution

 a first numerical approximation

 a second numerical approximation

 4.2 classification of differential equations

 4.3 the biack-scholes equation

 4.3.1 explicit, implicit, and o-methods

 4.3.2 initial and boundary conditions and definition of the grid

 4.3.3 implementation of the o-method with matlab

 4.3.4 stability

 4.3.5 coordinate transformation of space variables

 4.4 american options

 4.a a note on matlab's function spdiags

5. binomial trees

 5.1 motivation

 matching moments

 5.2 growing the tree

 5.2.1 implementing a tree

 5.2.2 vectorization

 5.2.3 binomial expansion

 5.3 early exercise

 5.4 dividends

 5.5 the greeks

 greeks from the tree

 part two simulation

6. generating random numbers

 6.1 monte carlo methods and sampling

 6.1.1 how it all began

 6.1.2 financial applications

 6.2 uniform random number generators

 6.2.1 congruential generators

 6.2.2 mersenne twister

 6.3 nonuniform distributions

 6.3.1 the inversion method

 6.3.2 acceptance-rejection method

 6.4 specialized methods for selected distributions

 6.4.1 normal distribution

 6.4.2 higher order momcnts and the cornish-fisher expansion

 6.4.3 further distributions

 6.5 sampling from a discrete set

 6.5.1 discrete uniforal selection

 6.5.2 roulette wheel selection

 6.5.3 random permutations and shuffling

 6.6 sampling errors---and how to reduce them

 6.6.1 the basic problem

 6.6.2 quasi-monte carlo

 6.6.3 stratified sampling

 6.6.4 variance reduction

 6.7 drawing from empirical distributions

 6.7.1 data randomization

 6.7.2 bootstrap

 6.8 controlled experiments and experimental design

 6.8.1 replicability and ceteris paribus analysis

 6.8.2 available random number generators in matlab

 6.8.3 uniform random numbers from matlab's rand function

 6.8.4 gaussian random numbers from matlab's randn function

 6.8.5 remedies

7. modeling dependencies

 7.1 transformation methods

 7.1.1 linear correlation

 7.1.2 rank correlation

 7.2 markov chains

 7.2.1 concepts

 7.2.2 the metropolis algorithm

 7.3 copula models

 7.3.1 concepts

 7.3.2 simulation using copulas

8. a gentle introduction to financial simulation

 8.1 setting the stage

 8.2 single-period simulations

 8.2.1 terminal asset prices

 8.2.2 1-over-n portfolios

 8.2.3 european options

 8.2.4 var of a covered put portfolio

 8.3 simple price processes

 8.4 processes with memory in the levels of returns

 8.4.1 efficient versus adaptive markets

 8.4.2 moving averages

 8.4.3 autoregressive models

 8.4.4 autoregressive moving average (arma) models

 8.4.5 simulatingarma models

 8.4.6 models with long-term memory

 8.5 time-varying volatility

 8.5.1 the concepts

 8.5.2 autocorrelated time-varying volatility

 8.5.3 simulating garch processes

 8.5.4 selected further autoregressive volatility models

 8.6 adaptive expectations and patterns in price processes

 8.6.1 price-earnings models

 8.6.2 models with learning

 8.7 historical simulation

 8.7.1 backtesting

 8.7.2 bootstrap

 8.8 agent-based models and complexity

9. financial simulation at work: some case studies

 9.1 constant proportion portfolio insurance (cppi)

 9.1.1 basic concepts

 9.1.2 bootstrap

 9.2 var estimation with extreme value theory

 9.2.1 basic concepts

 9.2.2 scaling the data

 9.2.3 using extreme value theory

 9.3 option pricing

 9.3.1 modeling prices

 9.3.2 pricing models

 9.3.3 greeks

 9.3.4 quasi-monte carlo

 part three optimization

10. optimization problems in finance

 10.1 what to optimize?

 10.2 solving the model

 10.2.1 problems

 10.2.2 classical methods and heuristics

 10.3 evaluating solutions

 10.4 examples

 portfolio optimization with alternative risk measures

 model selection

 robust/resistant regression

 agent-based models

 calibration of option -pricing models

 calibration of yield structure models

 10.5 summary

11. basic methods

 11.1 finding the roots off(x) = 0

 11.1.1 a naive approach

 graphical solution

 random search

 11.1.2 bracketing

 11.1.3 bisection

 11.1.4 fixed point method

 convergence

 11.1.5 newton's method

 comments

 11.2 classical unconstrained optimization

 convergence

 11.3 unconstrained optimization in one dimension

 11.3.1 newton's method

 11.3.2 golden section search

 11.4 unconstrained optimization in multiple dimensions

 11.4.1 steepest descent method

 11.4.2 newton's method

 11.4.3 quasi-newton method

 11.4.4 direct search methods

 11.4.5 practical issues with matlab

 11.5 nonlinear least squares

 11.5.1 problem statement and notation

 11.5.2 gauss-newton method

 11.5.3 levenberg-marquardt method

 11.6 solving systems of nonlinear equations f (x) = 0

 1 1.6.1 general considerations

 11.6.2 fixed point methods

 11.6.3 newton's method

 11.6.4 quasi-newton methods

 11.6.5 further approaches

 11.7 synoptic view of solution methods

12. heuristic methods in a nutshell

 12.1 heuristics

 12.2 trajectory methods

 12.2.1 stochastic local search

 12.2.2 simulated annealing

 12.2.3 threshold accepting

 12.2.4 tabu search

 12.3 population-based methods

 12.3.1 genetic algorithms

 12.3.2 differential evolution

 12.3.3 particle swarm optimization

 12.3.4 ant colony optimization

 12.4 hybrids

 12.5 constraints

 12.6 the stochastics of heuristic search

 12.6.1 stochastic solutions and computational resources

 12.6.2 an illustrative experiment

 12.7 general considerations

 12.7.1 what technique to choose?

 12.7.2 efficient implementations

 12.7.3 parameter settings

 12.8 summary

 12.a implementing heuristic methods with matlab

 12.a.1 threshold accepting

 12.a.2 genetic algorithm

 12.a.3 differential evolution

 12.a.4 particle swarm optimization

13. portfolio optimization

 13.1 the investment problem

 13.2 the dassical case: mean-variance optimization

 13.2.1 the model

 13.2.2 solving the model

 13.2.3 mean-variance models

 13.2.4 true, estimated, and realized frontiers

 13.2.5 repairing matrices

 13.3 heuristic optimization of one-period models

 13.3.1 asset selection with local search

 13.3.2 scenario optimization with threshold accepting

 13.3.3 examples

 13.3.4 diagnostics

 13.a more implementation issues in r

 13.a.1 scoping rules in r and objective functions

 13.a.2 vectorized objective functions

14. econometric models

 14.1 term structure models

 14.1.1 yield curves

 14.1.2 the nelson-siegel model

 14.1.3 calibration strategies

 14.1.4 experiments

 14.2 robust and resistant regression

 14.2.1 the regression model

 14.2.2 estimation

 14.2.3 an example

 14.2.4 numerical experiments

 14.2.5 final remarks

 14.a maximizing the sharpe ratio

15. calibrating option pricing models

 15.1 implied volatility with black-scholes

 the smile

 15.2 pricing with the characteristic function

 15.2.1 a pricing equation

 15.2.2 numerical integration

 15.3 calibration

 15.3.1 techniques

 15.3.2 organizing the problem and implementation

 15.3.3 two experiments

 15.4 final remarks

 15.a quadrature rules for infinity

bibliography

index