Learning about profitability and dynamic cash management

We study a dynamic model of firm whose shareholders learn about its profitability and, face costs external financing and holding cash. The shareholders' problem involves notoriously challenging singular stochastic control with two-dimensional degenerate diffusion process. solve it by means an explicit construction value function, derive corporate life-cycle two stages: “probation stage” where is never optimal for the to issue new shares, “mature resorts market whenever needed. cash target level nonmonotonic in belief reaches highest on edge between stages. This solution leads insights into firm's volatility payout ratio which depend stage life cycle.