Optimal Liquidity Management and Hedging in the presence of a non predictable investment opportunity

In this paper, we develop a dynamic model that captures the interaction between the cash reserves, the risk management policy and the profitability of a non-predictable irreversible investment opportunity. We consider a firm that has assets in place generating a stochastic cash- ow stream. The firm has a non-predictable growth opportunity to expand its operation size by paying a sunk cost. When the opportunity is available, the firm can finance it either by cash or by costly equity issuance. We provide an explicit characterization of the firm strategy in terms of investment, hedging, equity issuance and dividend distribution.

Numerical approximation of a cash-constrained firm value with investment opportunities

We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deterministic approximation of the related HJB variational inequality is provided. We finally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies.Comment: 30 pages, 10 figure