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雷达卡
我本科在澳洲没有学过高数，可是今年选了一个精算课，可是一看就发懵，哪位高人可以教教我这道题。太感谢了
The company plans to produce 1000000 oz of gold every 6 months for the next 2 years. Assume the gold is sold at the end of each half year.
The gold sales are made in $US. The company’s revenues are therefore subject to two separate market risks: the USD/AUD exchange rate, and the $US gold price.
suppose that Z1(t) and Z2(t) are Brownian motions with a correlation between increments over the same time interval given by correlation[{Z1(t)- Z1(s)}, { Z2(t)- Z2(s)} ]=p
But where increments over different (non overlapping) time intervals are independent. ie correlation [{Z1(T)- Z1(S)}, { Z2(t)- Z2(s)} ]=0 if the intervals (S,T) and (s,t) don’t overlap
Show that
αZ1(t) +βZ2(t) behaves like a Brownian motion αZ1(t) +βZ2(t)=УZ3(t)
Where У^2= α^2 +β^2 +2αβ
Hints: consider the properties of Brownian motion ( start at zero, independent increment. Zero mean, variance = t at time t and so on, check that the sum αZ1(t) +βZ2(t) has these properties.)
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