Home Assignment: Stochastic Calculus
Submit your solution (one per group) via Smart LMS (or to idergunov@hse.ru) before 11am on Thurs-
day, November 30. Please list your name on each of the documents you are submitting. Please prepare
handwritten notes, or use Word or Latex to type up your solutions. Before uploading your solutions,
scan your answers and save them as a pdf file, or convert your Word or Latex documents into pdf
files. If you find any typos in these assignment sheets, please contact me immediately.
The home assignment contributes 15% to the final grade for the course.
Optional exercises are denoted by ∗and are not compulsory to solve. Attempting to pro-
vide a solution/partial solution to such exercises as well as active in-class participation
during tutorials can give an additional benefit to the student towards the overall grade
of about 10%.
Exercise 1 [8 points]
What is the distribution generated by the following processes?
(a) dXt=rXtdt +σXtdWt
(b) dXt=adt −rdt +σdWt−τ2dWt
(c) Yt=Y0exp(µ−0.5σ2)t+σWt
(d) Xt=µt +νWt
