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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.

Let ${\left({\xi }_n\right)}_{n\ge 1}$ be the polygonal partial sums processes built on the linear processes $X_n={\sum }_{i\ge 0}{a}_i\left({ϵ}_{n-i}\right)$, ≥ 1, where ${\left({ϵ}_i\right)}_{i\in \mathbb{Z}}$ are i.i.d., centered random elements in some separable Hilbert space $ℍ$ and the 's are bounded linear operators $ℍ\to ℍ$, with ${\sum }_{i\ge 0}\parallel a_i\parallel <\infty$. We investigate functional central limit theorem for ${\xi }_n$ in the Hölder spaces ${\mathrm{H}}_{\rho }^o\left(ℍ\right)$ of functions $x:[0,1]\to ℍ$ such that || uniformly in , where , 0 ≤ ≤ 1 with 0 ≤ ≤ 1/2 and slowly varying at infinity. We obtain the ${\mathrm{H}}_{\rho }^o\left(ℍ\right)$ weak convergence of ${\xi }_n$ to some $ℍ$ valued Brownian motion...