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Display information for equation id:math.225934.23 on revision:225934

* Page found: Geometric Brownian motion (eq math.225934.23)

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Hash: 5b1a2539a34d6c64057c4d44533f16ee

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

MathML (12.774 KB / 1.804 KB) :

Cov ( S t i , S t j ) = S 0 i S 0 j e ( μ i + μ j ) t ( e ρ i , j σ i σ j t - 1 ) Cov superscript subscript 𝑆 𝑡 𝑖 superscript subscript 𝑆 𝑡 𝑗 superscript subscript 𝑆 0 𝑖 superscript subscript 𝑆 0 𝑗 superscript 𝑒 subscript 𝜇 𝑖 subscript 𝜇 𝑗 𝑡 superscript 𝑒 subscript 𝜌 𝑖 𝑗 subscript 𝜎 𝑖 subscript 𝜎 𝑗 𝑡 1 {\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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    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\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)}</annotation>
  </semantics>
</math>

SVG (16.49 KB / 5.02 KB) :

upper C o v times left-parenthesis upper S Subscript t Superscript i Baseline comma upper S Subscript t Superscript j Baseline right-parenthesis equals upper S 0 Superscript i Baseline times upper S 0 Superscript j Baseline times e Superscript left-parenthesis mu Super Subscript i Superscript plus mu Super Subscript j Superscript right-parenthesis times t Baseline times left-parenthesis e Superscript rho Super Subscript i comma j Superscript times sigma Super Subscript i Superscript times sigma Super Subscript j Superscript times t Baseline minus 1 right-parenthesis

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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)

Information about the conversion process:

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)

Information about the conversion process:

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


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