 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2019

Paper 203

Put
$$
p=\frac{8-\kappa}{8}>0,
\qquad q=\frac{8-\kappa}{\kappa}>0,
$$
so $M_t=\Upsilon_t^{-p}S_t^q$. Before $\tau_\epsilon$, one has $\Upsilon_t\geq\epsilon$ and $0<S_t\leq1$. Therefore
$$
0\leq M_{t\wedge\tau_\epsilon}\leq\epsilon^{-p}.
$$
The supplied continuous local martingale is thus bounded after stopping, and a bounded local martingale is a true martingale. Hence
$$
\boxed{(M_{t\wedge\tau_\epsilon})_{t\geq0}
\text{ is a bounded martingale}.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 203 / 2 / c / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 203 / 2 / c / i / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 203 / 2 / c / i / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)