2 At the beginning of each year, a firm observes its asset position (call it

d) and may invest any amount x (0  x 

d) in a risky investment. During each year, the money invested doubles with probability p and is completely lost with probability 1  p. Independently of this investment, the firm’s asset position increases by an amount y with probability qy (y may be negative). If the firm’s asset position is negative at the beginning of a year, it cannot invest any money during that year. The firm initially has $10,000 in assets and wants to maximize its expected asset position ten years from now. Formulate a dynamic programming recursion that will help accomplish this goal.