Analytical Solution of Special SDEs Apply Itos lemma to show a) Xt = exp Wt 1

Analytical Solution of Special SDEs Apply Itˆo’s lemma to show

a) Xt = exp

λWt − 1 2λ2t

 solves dXt = λXt dWt

b) Xt = exp(2Wt − t) solves dXt = Xt dt + 2Xt dWt Hint: Use suitable functions g with Yt = g(Xt,t). In

(a) start with Xt = Wt and g(x,t) = exp(λx − 1 2λ2t).