market model for mfBm

$z_0$ keszpenz
$z_{i}1\le i\le d$ pozicio az $i$-edik reszvenyben

$\varphi :{\mathbb{R}}^{+}\to {\mathbb{R}}^d$
$S:{\mathbb{R}}^{+}\to {\mathbb{R}}^d$

$t$-edik idopillanatban a keszpenz

$$X_t^0(\varphi )=z_0-{\int }_0^t{\varphi }_u\cdot S_{u}du-{\int }_0^t\lambda \Vert {\varphi }_u{\Vert }^{\alpha }du,$$

ahol $\alpha =2$ es ${\varphi }_u\cdot S_u$ a skalaris szorzast jeletni es $\Vert \cdot \Vert$ a kettes norma.

$t$-edik idopillanatban a $k$-adik reszvenyben a pozicio:

$$X_t^k(\varphi )=z_k+{\int }_0^t{\varphi }_{u}du$$ $$\mu =0$$ $$\theta =1$$ $$\sigma =1$$