Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases

Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases

Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases

Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases

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

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