Geodesic
Hedging of options with a given probability
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 152-161

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We consider a model of a complete market with two assets under the suggestion that an investor may hedge the payoff function with the given probability; in other words, the investor should have capital not less than the given payoff function with probability not less than $1-\alpha$ ($\alpha $ is a given significance level). Under some limitations on a class of hedging strategies we find a lower bound for an option price (that is, for the initial capital of the investor) and construct a hedge (the investor strategy) for which this lower bound is achieved. For examples, we calculate the price and hedge of a European call option and also an American call option with a barrier condition.
Keywords: financial mathematics, likelihood ratio, contingent claims.
Mots-clés : martingales 
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     author = {A. A. Novikov},
     title = {Hedging of options with a given probability},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {152--161},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a10/}
}
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A. A. Novikov. Hedging of options with a given probability. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 152-161. http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a10/