Suppose that in the absence of intervention, the cash on hand for a certain corp

Question

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 Greaterthanorequalto 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 long term 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?

Explanation / Answer

the fraction for cash interventions that are investments of excess cash is 3/4

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