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Numerical Methods and Optimization in Finance

介绍在金融工程应用的数值算法和优化技术,有实际的程序代码,是本很好的应用书
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“Gilli 01-fm-i-iv-9780123756626” — 2011/7/4 — page i — #1
Numerical Methods and
Optimization in Finance

“Gilli 01-fm-i-iv-9780123756626” — 2011/7/4 — page iii — #3
Numerical Methods and
Optimization in Finance
Manfred Gilli
University of Geneva and Swiss Finance Institute
Dietmar Maringer
University of Basel and University of Geneva
Enrico Schumann
VIP Value Investment Professionals AG, Switzerland
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Academic Press is an imprint of Elsevier

“Gilli 01-fm-i-iv-9780123756626” — 2011/7/5 — page 4 — #4
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“Gilli 03-loa-xiii-xiv-9780123756626” — 2011/7/4 — page xiii — #1
List of Algorithms
1 Forward substitution 37
2 Back-substitution 38
3 Cholesky factorization 42
4 Jacobi iteration 46
5 Gauss–Seidel iteration 46
6 SOR method 48
7 General structure of iterative methods 50
8 Block Jacobi method 52
9 Factorization of tridiagonal matrix 54
10 Forward and back-substitution for tridiagonal system 54
11 Least Squares with normal equations 63
12 Pseudocode for how \ works in Matlab 68
13 θ-method 82
14 Projected successive overrelaxation (PSOR) 92
15 Explicit payout method (EP) 93
16 European call for S, X , r , σ, T , and M time steps 106
17 Testing for early exercise: An American put 110
18 American call for S, X , r , σ, T , T
D
, D and M time steps 112
19 Linear congruential random number generator 122
20 Simplified acceptance–rejection for standard normal variates 129
21 Taylor–Thompson algorithm 151
22 Generate variates with specific rank correlation 169
23 Metropolis algorithm 176
24 Metropolis–Hastings 178
25 Direct sampling 184
26 Monte Carlo simulation for a European call option 192
27 Agent-based simulation of prices in a market with chartists and fundamentalists 231
28 One-pass algorithm for computing the variance 250
29 Bracketing 290
30 Bisection 291
31 Fixed point iteration 292
32 Newton’s method for zero finding 298
33 Newton’s method for unconstrained optimization 304
34 Golden section search 305
35 Steepest descent method 307
36 Newton’s method for unconstrained optimization in n dimensions 309
37 Quasi-Newton for unconstrained optimization in n dimensions 311
38 Nelder–Mead simplex direct search 316
39 Gauss–Newton method 320
40 Levenberg–Marquardt method 320
xiii

“Gilli 03-loa-xiii-xiv-9780123756626” — 2011/7/4 — page xiv — #2
xiv List of Algorithms
41 Jacobi, Gauss–Seidel, and SOR for nonlinear systems 326
42 Newton’s method for nonlinear systems 329
43 Broyden’s method for nonlinear systems 333
44 Local search 342
45 Simulated Annealing 343
46 Threshold Accepting 344
47 Tabu Search 345
48 Genetic Algorithms 346
49 Differential Evolution 347
50 Particle Swarm Optimization 348
51 Ant Colony Optimization 349
52 Repair mechanism for correlation matrix 400
53 Local Search for asset selection 404
54 Neighborhood (asset selection) 407
55 Threshold Accepting 417
56 Computing the threshold sequence—Variant 1 420
57 Computing the threshold sequence—Variant 2 420
58 Neighborhood (budget constraint) 422
59 Neighborhood (holding sizes) 423
60 Threshold Accepting—scenario updating 428
61 Neighborhood (budget constraint, cardinality constraints) 432
62 Differential Evolution for yield curve models 459
63 Particle Swarm Optimization for robust regression 487
64 Computing the prices for a given surface 537
65 Hybrid search 542
66 Repairing a solution x by reflection 551
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