Write in general the DP equation for the problem formulated in Exercise 13.

Suppose that at time 0 , the share price \(x_{0}=\$ 5\). The investor holds exactly 10 shares initially and the checking account starting balance is \(y=\$ 50\). Interest rates are \(u=.08\) and \(d=-.05\). The investor wants to maximize wealth at the end of 3 years assuming that \(q=.5\). Write the DP equation using these parameter values and draw a tree diagram representing the possible paths of the risky asset.