ACT460H1 Chapter 2: PS2
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Stochastic methods for actuarial science - problem set #2 due nov, 17 at 2pm. Grad students also hand in questions marked with +: suppose that wt and zt are correlated wiener processes with instantaneous correlation . Find the mean and variance of each of the following random variables (t is xed and positive): (a) w1 + w2 + . + wn for n n. (b) exp{wt }. (c) a wt + b zt . (d) [**] exp{a wt + b zt }. (e) wt zt . (f) [**] r t. 0 ws zs ds: suppose that wt and zt are standard correlated wiener processes with instantaneous correlation. For each of the following (i) compute the mean and variance of yt and (ii) derive an integration by parts formulae: 0 zs dws = wt zt t. 0 ws dzs +r t: assume that the prices of two stocks st and ut satisfy the following coupled sdes: dut.
