Optimal Cash Management Under Uncertainty

The problem of optimal investment in two types of assets over time is formulated as a stochastic optimal control problem. The two assets considered are a bank account and stock. The earnings derived from stock consist of dividends and capital gains. The randomness in the return on stock is modeled using a standard Brownian motion. Using a stochastic maximum principle, an explicit decision rule of the bang-bang type is derived for optimal management of cash.