Optimal investment facing possible accidents

This paper studies the optimal behavior of a firm over time that faces the probability of causing an environmental disaster by its activities. Here we can think of explosions in the chemical industry, oil tankers that lose oil, etc. In the static literature a distinction is made between small firms and large firms. Small firms are called undercapitalized in the sense that the share holders are not willing to pay for the accident because of the reason that the accidental damage exceeds the value of the firm. As soon as this happens the firm is declared bankrupt. This gives an incentive to spend part of the safety budget on distributing dividends to the shareholders under the motto: pay dividends as long as it is still possible. In this paper we extend the static framework to a dynamic one. The major reason is to find out under what circumstances it can be optimal for a small firm to expand in order to become a large firm that has the means to fully pay for the damage caused by an environmental accident. Admittedly, this paper is only a first step in reaching this goal. Here, we determine the optimal safety expenditures and the convergence behavior of long run investment policies.