Study On Strategy Of Firm Abatement Investment

As China attaches more importance on environmental protection, environmental strategy is gradually improved. Some places have begun to implement tradable pollution permits system. This market-oriented environmental strategy makes clear that firms'abatement investment is significant. Hence study on firms'abatement investment is getting meaningful.The paper begins with analysis under certainty, and then extends to problems under uncertainty. Under certainty, when the product price and permits price are fixed, a model targeting firm value maximization as the object function is constructed in a dynamic framework. The optimal conditions and growth path of abatement investment are further got by applying optimal control means. According to optimal condition, capital's shadow price shall always equal to the marginal investment cost. And according to optimal path, when existing abatement capital is very little, the optimal strategy will start from a higher investment rate, and then decrease monotonously until reaching the steady point. Otherwise, its optimal path is contrary.Based on discussion under certainty, this paper further analyzes firm's strategy under uncertainty from two aspects, i.e. uncertainty on output price or tradable permits price. Under the former circumstance, the paper assumes product price is subject to geometric Brownian motion while permits price is fixed, and accordingly constructs dynamic model of value maximization. And by using dynamic programming method, a stochastic differential equations is established based on Ito's Lemma, thus a HJB equation is got. Finally, based on the HJB equation and combining with the optimal stopping methodologies, the free boundary of the product price is obtained. If the product price remains under the boundary, there's no need for the firm to increase the abatement investment. It is the optimal strategy to maintain the current accumulated investment. Once it exceeds the boundary, the firm ought to increase abatement investment immediately.For the instance of tradable permits price uncertainty, in terms of unpredictable environmental policy changes, two situations should be considered, continuous fluctuation and jumping fluctuation, characterized by geometric Brownian motion and combination of Brownian motion and Poisson process respectively. The analyzing method is the same as the product price uncertainty situation. The free boundary of permits price is finally obtained. Similarly, if permits price exceeds the free boundary, new abatement investment should be implemented immediately.