Homework Help: Martingale problem: help writing and equation using the martingale assumptions

1. Mar 7, 2012

Nyn

Hi,

I have been given this problem and the solution however, neither make sense to me.

$$x_t=\int exp(t-s)E(k_s|F_t)ds$$

(the integral is from t to infinity)

where

$$k_u=m^d_u-(m^d_u)^*-α(y_u-y_u^*)$$ for all u>0

suppose (m_t, t>0) is a martingale, what is an equation for x_t using the martingale assumption for (m_t, t>0).

the solutions say

$$E_tk_s^2=m_t+E_t(-m_s^*-α(y_s-y_s^*))=m_t+v_s. thus, x_t=m_t+ \int v_s de$$

So, first off I don't know what the martingale assumptions are a simple google search did not yield any useful results. Secondly I can't seem to follow the math (it's been a while since I have done anything other that simple integration).

I am hoping that someone is familiar with the martingale assumptions and can explain this problem to me-or maybe knows about a cite with a good beginners explanation to the topic.

Thanks,