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Year 2 of the mathematics and statistics course of the University of Oxford

Probability, statistics and options II course of the University of Oxford

Past exam of the Probability, statistics and options II course of the University of Oxford

2009

Since a Poisson count has mean and <variance> $\lambda t$, substitute the centering and scaling into its moment generating function:
$$
\boxed{M_{U_t}(\theta)=\exp\left\{\lambda t\left(e^{\theta/\sqrt{\lambda t}}-1-\frac\theta{\sqrt{\lambda t}}\right)\right\}.}
$$
This is finite for every real $\theta$ when $t>0$.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / M / M4 / e / i / Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / M / M4 / e / i / Solution

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Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / M / M4 / e / i / Solution

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