We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we sh...

A The auxiliary problem 1 A.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A.2 Immediate liquidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A.3 Value of a barrier strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 3 A.4 The optimal barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 A.5 Verification . . . . . . ....

In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime s...

A The auxiliary problem 1 A.1. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A.2. Immediate liquidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A.3. Value of a barrier strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 3 A.4. The optimal barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 A.5. Verification . . . . ...

This paper presents a monetary model in which consumption and capital investment can undergo upswings and downturns in the presence of collateral constraints. When the collateralized asset has a liquidation value below its full value, we show that a stable cyclical equilibrium can emerge in consumption and capital investment around the unstable steady state.

This paper proposes a new pricing model for corporate securities issued by a levered firm with the possibility of debt renegotiation. We take the structural approach that the firm’s earnings follow a geometric Brownian motion with stochastic collaterals. While equity holders can default the firm for their own benefits when the earnings become insufficient to go on the firm, they may want to liq...

This paper studies whether and to what extent transparent disclosure prevents inefficient liquidation arising from rollover risk. We model an illiquid but solvent borrower who can design a public signal about what creditors can recover from forcing liquidation, and what their claims would be worth if the firm survives. We find that the signal structure that minimizes rollover risk never identif...