Geodesic
Financial Market with Interacting Assets. Pricing Barrier Options
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 173-184

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A new model of a financial market with several interacting assets is introduced and developed. The mutual interaction of asset prices is described by a general multidimensional linear stochastic differential equation with multiplicative noise. The non-arbitrage and completeness conditions for the model are studied in detail. As an application, the pricing of the outside barrier options and of the floating barrier options based on a 2-dimensional version of the model is considered. 
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     author = {S. A. Albeverio and V. R. Steblovskaya},
     title = {Financial {Market} with {Interacting} {Assets.} {Pricing} {Barrier} {Options}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_237_a7/}
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S. A. Albeverio; V. R. Steblovskaya. Financial Market with Interacting Assets. Pricing Barrier Options. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 173-184. http://geodesic.mathdoc.fr/item/TM_2002_237_a7/