1.7. Suppose that in the absence of intervention, the cash on hand for a certain corporation fluctuates according to a standard Brownian motion

{B(t); t ? 0 }. The company manages its cash using an (s, S) policy: If the cash level ever drops to zero, it is instantaneously replenished up to level s; If the cash level ever rises up to S, sufficient cash is invested in longterm securities to bring the cash-on-hand down to level s. In the long run, what fraction of cash interventions are investments of excess cash? Hint:

Use equation (1.13).