We consider multidimensional tree-based models of arbitrage-free and path-independent security markets. We assume that no riskless investment exists. Contingent claims pricing and hedging problems in such a market are studied.
@article{bwmeta1.element.bwnjournal-article-zmv26i3p253bwm, author = {Remigijus Leipus and Alfredas Ra\v ckauskas}, title = {Security price modelling by a binomial tree}, journal = {Applicationes Mathematicae}, volume = {26}, year = {1999}, pages = {253-266}, zbl = {1050.91515}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv26i3p253bwm} }
Leipus, Remigijus; Račkauskas, Alfredas. Security price modelling by a binomial tree. Applicationes Mathematicae, Tome 26 (1999) pp. 253-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv26i3p253bwm/
[000] J. C. Cox, S. A. Ross and M. Rubinstein (1979), Option pricing: a simplified approach, J. Financial Econom. 7, 229-263. | Zbl 1131.91333
[001] J. M. Harrison and S. Pliska (1981), Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl. 11, 215-260. | Zbl 0482.60097
[002] J. Jacod and A. N. Shiryaev (1998), Local martingales and the fundamental asset pricing theorems in the discrete-time case, Finance Stochastics 2, 259-273. | Zbl 0903.60036
[003] B. A. Jensen and J. A. Nielsen (1996), Pricing by 'No arbitrage', in: Time Series Models in Econometrics, Finance and Other Fields, D. R. Cox et al. (eds.), Chapman & Hall, London, 177-223.
[004] Yu. M. Kabanov and D. O. Kramkov (1994), No-arbitrage and equivalent martingale measures: an elementary proof of the Harrison-Pliska theorem, Theory Probab. Appl. 39, 635-640. | Zbl 0834.60045
[005] D. Lamberton and B. Lapeyre (1996), Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, London. | Zbl 0949.60005
[006] J. B. Long Jr. (1990), The numeraire portfolio, J. Financial Econom. 26, 29-69.
[007] M. Motoczyński and Ł. Stettner (1998), On option pricing in the multidimensional Cox-Ross-Rubinstein model, Appl. Math. (Warsaw) 25, 55-72. | Zbl 0895.90016