I think I am working this problem correctly, but want to make sure I actually am understanding the material.

2. Consider the an asset pricing model where the agent maximizes expected discounted (by B) lifetime utility (period utility is u(ct)). Each period, the agent must fund con- sumption and new net purchase shares (P.(St+1 - st)) from the dividends of previously held shares which pay a period dividend of de. Note that p, is the price of the stock. The period t budget is: dist = Ct + Pt (St+1 - St) . Suppose that dividends follow a stochastic process of: In dt+1 - (1 - pa) Ind - palndt - Ed,t+1. (a) Write out the infinite dimension problem faced by the household. (b) Now, write out the problem in dynamic programming style by finding the Bell- man's equation. Be sure note all 7 elements of DP problem (hint: let the time t states be St = {dt, P:})