- Joined
- 8/24/11
- Messages
- 173
- Points
- 278
Hey,
Find the values for p where (dx(t)=(-r+pr+\frac{1}{2}p(p-1)\sigma^2)x(t)dt+p\sigma x(t)dW(t)) is a martingale?
Why can't I say that if the process has zero drift then it's a martingale and solve ((-r+pr+\frac{1}{2}p(p-1)\sigma^2)=0)? or how should I go about this - is the only way, to use the properties of a martingale and show for which p the conditions are fulfilled or is there an easier way?
(The question is a subpart of another question where I found an SDE:
(dY(t)=(pr+\frac{1}{2}p(p-1)\sigma^2)Y(t)dt+p\sigma Y(t)dW(t))
and I have to find the values for p where (exp(-rt)Y(t)) is a martingale so I define (x(t)=exp(-rt)Y(t)) and use Ito, to get
(dx(t)=(-r+pr+\frac{1}{2}p(p-1)\sigma^2)x(t)dt+p\sigma x(t)dW(t)))
Find the values for p where (dx(t)=(-r+pr+\frac{1}{2}p(p-1)\sigma^2)x(t)dt+p\sigma x(t)dW(t)) is a martingale?
Why can't I say that if the process has zero drift then it's a martingale and solve ((-r+pr+\frac{1}{2}p(p-1)\sigma^2)=0)? or how should I go about this - is the only way, to use the properties of a martingale and show for which p the conditions are fulfilled or is there an easier way?
(The question is a subpart of another question where I found an SDE:
(dY(t)=(pr+\frac{1}{2}p(p-1)\sigma^2)Y(t)dt+p\sigma Y(t)dW(t))
and I have to find the values for p where (exp(-rt)Y(t)) is a martingale so I define (x(t)=exp(-rt)Y(t)) and use Ito, to get
(dx(t)=(-r+pr+\frac{1}{2}p(p-1)\sigma^2)x(t)dt+p\sigma x(t)dW(t)))