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Let ( S ) be the value of a stock that evolves according to ( mathrm{d} S=mu S mathrm{~d} t+sigma S mathrm{~d} B ). A

image text in transcribed Let \\( S \\) be the value of a stock that evolves according to \\( \\mathrm{d} S=\\mu S \\mathrm{~d} t+\\sigma S \\mathrm{~d} B \\). A \"cubic contract\" has a payoff at expiration of \\( V_{T}=\\left(S_{T}\ ight)^{3} \\). What is the value \\( V_{0} \\) of the contract at \\( t=0 \\) ? Express your answer in terms of \\( r, T, \\quad \\) for \\( \\sigma, \\quad \\) for \\( \\mu \\), and \\( S_{-} 0 \\) for \\( S_{0} \\), as needed

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