Exercise 15.4.1 Suppose that S1, S2, . . . , Sn pay no dividends and follow dSi /Si =

μi dt +σi dWi . Let ρjk denote the correlation between dWj and dWk. Show that

∂ f

∂t

+

i

(μi −λiσi ) Si

∂ f

∂Si

+ 1 2

i k

ρikσiσkSi Sk

∂2 f

∂Si ∂Sk

= r f (15.14)

when the derivative f depends on more than one state variable S1, S2, . . . , Sn.