Math 489/889 Final Name:________________________________
Thursday, December 17, 2009
Problem | 1 | 2 | 3 | 4 | 5 | 6 | Total |
Possible | 15 | 25 | 20 | 20 | 30 | 10 | 120 |
Points | |||||||
(Remark: With some general parameters, this stochastic differential equation is a model of a “mean-reverting square-root process that models asset prices”.) Use $dt=0.2$, the table of net totals of randomly generated coin flips below, and recall that as in the notes $dW\approx \sqrt{dt}\left(S\left(Ndt\right)\u2215\sqrt{Ndt}\right)$.
$j$ | ${X}_{j}$ | $\left(1-{X}_{j}\right)$ | $\sqrt{{X}_{j}}$ | $\left(1-{X}_{j}\right)\phantom{\rule{0em}{0ex}}dt+\sqrt{{X}_{j}}\phantom{\rule{0em}{0ex}}dW$ | ${X}_{j+1}$ |
0 | |||||
1 | |||||
2 | |||||
3 | |||||
4 | |||||
5 | |||||
$n$ | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
${S}_{n}$ | 0 | -4 | -6 | -10 | -8 | -8 | -6 | -8 | -6 | -10 | -8 |