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TeX (original user input):

\mathrm{Cov}(S_{t}^i, S_{t}^j) = S_0^i S_0^j e^{(\mu_i + \mu_j) t }\left(e^{\rho_{i,j} \sigma_i \sigma_j t}-1\right)


TeX (checked):

\mathrm {Cov} (S_{t}^{i},S_{t}^{j})=S_{0}^{i}S_{0}^{j}e^{(\mu _{i}+\mu _{j})t}\left(e^{\rho _{i,j}\sigma _{i}\sigma _{j}t}-1\right)


### LaTeXML (experimental; uses MathML) rendering

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${\displaystyle{\mathrm{Cov}}(S_{{t}}^{i},S_{{t}}^{j})=S_{0}^{i}S_{0}^{j}e^{{(% \mu_{i}+\mu_{j})t}}\left(e^{{\rho_{{i,j}}\sigma_{i}\sigma_{j}t}}-1\right)}$
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${\displaystyle \mathrm {Cov} (S_{t}^{i},S_{t}^{j})=S_{0}^{i}S_{0}^{j}e^{(\mu _{i}+\mu _{j})t}\left(e^{\rho _{i,j}\sigma _{i}\sigma _{j}t}-1\right)}$

## Translations to Computer Algebra Systems

### Translation to Maple

In Maple: C*(S(S[t])^(i), S(S[t])^(j))= (S[0])^(i)*(S[0])^(j)*(e)^((mu[i]+ mu[j])* t)*((e)^(rho[i , j]*sigma[i]*sigma[j]*t)- 1)

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Maple uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit

e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

exp(1): You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Maple uses exp(1) for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe

i: the imaginary unit == the principal square root of -1 was translated to: i

### Translation to Mathematica

In Mathematica: C*(S(Subscript[S, t])^(i), S(Subscript[S, t])^(j))= (Subscript[S, 0])^(i)*(Subscript[S, 0])^(j)*(e)^((Subscript[\[Mu], i]+ Subscript[\[Mu], j])* t)*((e)^(Subscript[\[Rho], i , j]*Subscript[\[Sigma], i]*Subscript[\[Sigma], j]*t)- 1)

E: You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Mathematica uses E for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Mathematica uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit

e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

i: the imaginary unit == the principal square root of -1 was translated to: i

## Similar pages

Calculated based on the variables occurring on the entire Geometric Brownian motion page

## Identifiers

• ${\displaystyle \mathrm {Cov} }$
• ${\displaystyle S}$
• ${\displaystyle t}$
• ${\displaystyle i}$
• ${\displaystyle S}$
• ${\displaystyle t}$
• ${\displaystyle j}$
• ${\displaystyle S}$
• ${\displaystyle i}$
• ${\displaystyle S}$
• ${\displaystyle j}$
• ${\displaystyle e}$
• ${\displaystyle \mu _{i}}$
• ${\displaystyle \mu _{j}}$
• ${\displaystyle t}$
• ${\displaystyle e}$
• ${\displaystyle \rho _{i,j}}$
• ${\displaystyle \sigma _{i}}$
• ${\displaystyle \sigma _{j}}$
• ${\displaystyle t}$

### MathML observations

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