Geodesic
An algorithmic approach to non-self-financing hedging in a discrete-time incomplete market
Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 140-159 
N. Josephy; L. Kimball; V. R. Steblovskaya; A. V. Nagaev; M. Pasnievskii. An algorithmic approach to non-self-financing hedging in a discrete-time incomplete market. Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 140-159. http://geodesic.mathdoc.fr/item/DM_2007_19_3_a10/
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     title = {An algorithmic approach to non-self-financing hedging in a~discrete-time incomplete market},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimisation is a two stage process that first determines admissible model parameters that correspond to the market price of the option being hedged. The second stage applies various merit functions to bootstrapped samples of model residuals to choose an optimal set of model parameters from the admissible set. Results are presented for options traded on the New York Stock Exchange.

[1] Tessitore G., Zabczyk J., “Pricing options for multinomial models”, Bull. Polish Acad. Sci. Math., 44:3 (1996), 363–380 | MR | Zbl

[2] Wolczynska G., “An explicit formula for option pricing in discrete incomplete markets”, Intern. J. Theoret. Appl. Finance, 1:2 (1998), 283–288 | DOI | Zbl

[3] Hammarlid O., “On minimizing risk in incomplete markets”, Intern. J. Theoret. Appl. Finance, 1:2 (1998), 227–233 | DOI | Zbl

[4] Ryushendorf L., “On upper and lower prices in discrete time models”, Trudy Matem. in-ta im. V. A. Steklova, 237 (2002), 134–139 | MR

[5] Nagaev A., Nagaev S., “Asymptotics of riskless profit under selling of discrete time call options”, Appl. Math., 30:2 (2003), 173–191 | MR | Zbl

[6] Nagaev A. V., Nagaev S. V., Kunst R., A diffusion approximation to the Markov chain model of the financial market and the expected riskless profit under selling of call and put options, Preprint 164, Economics Series, Institute for Advanced Studies, Vienna, 2005

[7] Nagaev A. V., Nagaev S. V., Kunst R., A diffusion approximation to the riskless profit under selling of discrete time call options: Non-identically distributed jumps, Preprint 164, Economics Series, Institute for Advanced Studies, Vienna, 2005

[8] Jouini M. M. E., Cvitanic J., Option pricing, interest rates and risk management, Cambridge Univ. Press, Cambridge, 2001 | MR

[9] Shiryaev A. N., Osnovy stokhasticheskoi finansovoi matematiki, t. 1, 2, FAZIS, Moskva, 1998

[10] Melnikov A. V., Volkov S. N., Nechaev M. L., Matematika finansovykh obyazatelstv, GU VShE, Moskva, 2001

[11] Sarykalin S., Uryasev S., “Pricing derivative securities in incomplete markets”, Proc. 36th Conf. on Winter Simulation, IEEE, Piscataway, NJ, 2004, 1586–1588