Using Value-at-Risk to reconcile limited liability and the moral-hazard problem

In the present paper uncertainty over the market price of a risk-neutral competitive firm’s output and limited liability imply the possibility of bankruptcy, give rise to moral hazard and entail that the firm’s output decision depends on its equity holding. Subjecting the firm to a Value-at-Risk (VaR) constraint induces it to behave in an as-if risk-averse manner, but in a static context moral hazard persists for a certain interval of values of equity. In a dynamic setting, the size of equity holding becomes a choice variable and the VaR constraint guides the firm to select equity values outside the moral-hazard interval. Thus it achieves to reconcile two apparently conflicting goals: encourage entrepreneurial activity by means of limited liability and avoid irresponsible gambling due to the incentives provided by it.