Jeanblanc M., Yor M., Chesney M. Mathematical Methods for Financial Markets
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Subject Index 731
Reflection principle, 136
Regular diffusion, 270
Representation
L´evy-Khintchine, 593
Resolvent, 144
kernel, 277
of a Markov process, 17
Risk premium, 91, 94
Risk-neutral probability
Black and Scholes framework, 96
for DZC, 416
Running maximum, 41, 326
Scale function, 271
for a CEV, 371
for BESQ, 336
for Bessel processes, 274
for Brownian motion, 274
for Geometric BM, 274
for reflected Brownian motion, 274
for Vasicek process, 275
Scaling
for squared Bessel processes, 338
property for BM, 32
Securities, 80
Self-decomposable r.v., 596
Self-financing condition
with consumption, 64
Self-financing strategy, 81, 104, 544
Selling price, 575
Semi-group of an time-homogeneous
Markov process, 16
Semi-martingale, 27, 522
pseudo-continuous, 529
special, 522
Short-selling, 81
σ-algebra
optional, 512
predictable, 512
Smooth-fit principle, 196
Solution
strictly weak - for SDE, 43
strong - for SDE, 43
weak - for SDE, 43
Spectrally negative L´evy process, 632
Speed measure, 271
for a CEV, 371
for Brownian motion, 274
for Geometric BM, 274
for reflected Brownian motion, 274
Spread
credit, 410
Stable
process, 608
random variable, 598
State-price density, 93
Stieltjes integral, 510
Stochastic
exponential, 52, 617
logarithm, 533, 617
Stochastic Differential Equations
and mixed processes, 556
existence theorem, 43
Stop-Loss strategy, 229
Stopped process, 22
Stopping time, 21
predictable, 22, 513
pseudo, 24, 326, 430
totally inaccessible, 22, 513
Strategy
admissible, 85
hedging, 87
Stratonovich integral, 41, 51
Strict local martingale, 26, 77, 226,
336, 339, 341, 371, 372, 560
Strong solution for SDE, 43
Structure condition, 538
Structure equation, 522, 579, 580
Sturm-Liouville equation, 353
Subordinator, 600, 634
Super-replication price, 548, 575
Survival distribution
function, 409
Symmetry, 160
American boundaries, 198, 588
American put-call, 197
Asian option, 383
European put-call, 162
for Parisian options, 256
in a jump-diffusion model, 562
put-call - for mixed processes, 562,
588
Tanaka’s formulae
for Brownian motion, 214
Tanaka-Meyer formulae
for semi-martingales, 224
Tempered stable process, 640
732 Subject Index
Theorem
Cameron-Martin, 73
Doob’s optional sampling, 23
Doob-Meyer, 20
Dubins Schwarz, 261
Dudley, 60
Girsanov, 69, 73, 531
Girsanov - for a pair BM and PP ,
560
L´evy, 218
Lamperti, 347
Monroe, 263
Pitman, 307
Sklar, 423
Stochastic Fubini, 211
Time
changed, 260, 276, 347, 348, 357,
390, 395
Wiliams - reversal, 307
Time inversion, 32
Transition density
for a BES, 343
for a BESQ, 343
for a CIR, 358
Transition probability, 15
Tsirel’son example, 49
ucp convergence, 12
Uniform integrability, 18, 532
Uniformly integrable
martingale, 75, 532
Uniqueness
in law for SDE, 43
pathwise - for SDE, 43
Variance-Gamma process, 639
Version, 11
Volatility
implied, 392
local, 227
Watanabe’s characterization, 468
Wiener-Hopf factorization, 629
Williams’ time reversal result, 307
Wronskian, 278
Zero-coupon bond, 81
defaultable, 408
deterministic case, 408
in a CIR framework, 362
in an OU framework, 123