The variable S is an investment asset providing income at the rate q measured in currency A and it follows the process: dS = mu(subscript S)Sdt + sigma(subscript S)Sdz In the real world. Defining new variables as necessary, give the process followed by S, and the corresponding market price of risk, in:
1) A world that is the traditional risk-neutral world for Currency A
2) A world that is the traditional risk-neutral world for Currency B
3) A world that is forward risk-neutral world with respect to a zero-coupon currency A bond maturing at time T
4) A world that is forward risk-neutral world with respect to a zero-coupon currency B bond maturing at time T