The indifference valuation problem in incomplete binomial models is analyzed. The model is more general than the ones studied so far, because the stochastic factor, which generates the market incompleteness, may affect the transition propabilities and/or the values of the traded asset as well as the claim’s payoff. Two pricing algorithms are constructed which use, respectively, the minimal martingale and the minimal entropy measures. We study in detail the interplay among the different kinds of market incompleteness, the pricing measures and the price functionals. The dependence of the prices on the choice of the trading horizon is discussed. The family of “almost complete” (reduced) binomial models is also studied. It is shown that the two measures and the associated price functionals coincide, and that the effects of the horizon choice dissipate.

DOI: 10.5802/msia.4

^{1}; Sokolova, E.

^{2}; Zariphopoulou, T.

^{3}

@article{MSIA_2010__3_2_1_0, author = {Musiela, M. and Sokolova, E. and Zariphopoulou, T.}, title = {Indifference valuation in incomplete binomial models}, journal = {MathematicS In Action}, pages = {1--36}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {3}, number = {2}, year = {2010}, doi = {10.5802/msia.4}, mrnumber = {2725844}, zbl = {1204.91137}, language = {en}, url = {http://www.numdam.org/articles/10.5802/msia.4/} }

TY - JOUR AU - Musiela, M. AU - Sokolova, E. AU - Zariphopoulou, T. TI - Indifference valuation in incomplete binomial models JO - MathematicS In Action PY - 2010 SP - 1 EP - 36 VL - 3 IS - 2 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/msia.4/ DO - 10.5802/msia.4 LA - en ID - MSIA_2010__3_2_1_0 ER -

%0 Journal Article %A Musiela, M. %A Sokolova, E. %A Zariphopoulou, T. %T Indifference valuation in incomplete binomial models %J MathematicS In Action %D 2010 %P 1-36 %V 3 %N 2 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/msia.4/ %R 10.5802/msia.4 %G en %F MSIA_2010__3_2_1_0

Musiela, M.; Sokolova, E.; Zariphopoulou, T. Indifference valuation in incomplete binomial models. MathematicS In Action, Volume 3 (2010) no. 2, pp. 1-36. doi : 10.5802/msia.4. http://www.numdam.org/articles/10.5802/msia.4/

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