2500
4000
3500
3000
50 100 150 200 250
-200
1200
50 100 150 200 250
(a) Underlying asset: daily values during the last (b) Option: daily values during the last 223 days,
inria-00457222, version 1 - 16 Feb 2010
223 days, and trend (- -)
(c) Daily interest rate r
Figure 2: Example 1: CFU9PY3500
and trend (- -)
0 50 100 150 200 250
(d) ∆ tracking
[3] Black F., Scholes M., The pricing of options and corporate liabilities,
J. Political Economy, 3, 637-654, 1973.
[4] Cartier P., Perrin Y., Integration over finite sets, in Nonstandard
Analysis in Practice, F. & M. Diener (Eds), Springer, 1995, pp. 195-204.
[5] Cont R., Tankov P., Financial Modelling with Jump Processes, Chap-
man & Hall/CRC, 2004.
[6] Derman, E., Taleb N., The illusion of dynamic delta replication, Quan-
titative Finance, 5, 323-326, 2005.
[7] El Karoui N., Jeanbianc-Picque M., Shreve S., Robustness of the
Black and Scholes formula, Math. Finance, 8, 93-126, 1998.
[8] Fliess M., Join C., Commande sans mod`ele et commande a`
modèle restreint, e-STA, 5 (n° 4), 1-23, 2008, (available at
http://hal.inria.fr/inria-00288107/en/).
[9] Fliess M., Join C., A mathematical proof of the existence of trends in fi-
nancial time series, in Systems Theory: Modeling, Analysis and Control, A.
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