Exhaustible Resources And Optimal Exploiture Under Uncertainty

Exhaustible resource is such an important natural resource that the human being could not survive and then develop without it. Whether and how to achieve the sustainable development of exhaustible resources has become the major issue of current research on the sustainable development of the human society. All satisfactory results should be derived from precise evaluation and efficient exploiture of exhaustible resources. Prior studies on exhaustible resources exploiture usually pay little attention to the effects of unexpected events and the non-renewability of exhaustible resources which have been proved to be of great importance by many empirical works in this field, suggesting a need for more appropriate approaches. Drawing upon the stochastic dynamic control theory and real option theory, the author establishes an optimal exploiture model of exhaustible resources under uncertainty. In order to highlight the crucial roles of unexpected events and non-renewability, this paper combines the time limit and jump processes into the model to analyze such problems as optimal mining timing, mining strategies, exhaustible resources market and environmental policy. The following conclusions can be drawn:1) The view that the prices of exhaustible resources follow a Geometric Brownian Motion is not consistent with the reality since jump process has great power in the fluctuation of exhaustible resources prices.2) The different forms of uncertainty have different effects on optimal mining timing. First, the larger the fluctuation resulting from continuous processes, the stronger the incentive of waiting is. Hence, the firm is more reluctant to invest. Second, the fluctuation resulting from discrete processes affects the firm's decision in two ways. One side, it reduces the expected proceeds from investing the mine; the other side, it also changes the risks of the investment. The optimal investment strategy would be determined by the more powerful one. An extended model, based on the above results, is considered to analyze the effects of variable output, sudden death and cost uncertainty on the optimal mining timing.3) By dividing the firm's strategies, such as exploiting, scrapping, mothballing and reactivation, into different sets as well as constructing the value functions in each set, the author shows the critical values above which the firm would change its strategy. If exhaustible resources have not been exploited, the more uncertainty, the stronger the incentive of waiting, which will lead the firm to slower the rate of mining. If exhaustible resources have been exploited, the more uncertainty, the higher the critical values, although the effects of such fluctuations would become weaker as the stock of resources decreases. Furthermore, these critical values are significantly affected by the jump process and non-renew ability, ignoring which would cause systematical errors.4) A stochastic dynamic programming model with jump processes could efficiently describe the uncertainty resulting from market demand and resource reserve, as well as the effects of exploration on the resources prices and mining rate. On the one hand, the reserve uncertainty will accelerate the rate at which prices increase. While the exploration will decrease the uncertainty and then pull down the price. On the other hand, although the demand uncertainty does not impact the price fluctuations, it will slower the exhausting speed of resources which would negatively affect the firm's expected profits. Thus, the producer should have to balance the loss due to future demand fluctuations against the proceeds from reserve fluctuations.5) The effects of policy uncertainty on the mining timing lie on whether the policy is favor of the firm gaining more benefits from mining. If yes, the more uncertain policy is, the slower mining will be. In contrast, the variation of policy will accelerate the speed of mining. 6) The standard framework to evaluate environmental policies is cost-benefit analysis. It may mislead when the framework ignores the uncertainty and irreversibilities of environmental problems and the policies designed to respond to them. This paper establishes a stochastic dynamic programming model and analyzes the optimal timing problems in environmental policy under uncertainty. Results indicate that there are two kinds of uncertainty influencing the timing of environmental policy implementation and they work in opposite directions: on the one hand, the more uncertain the economy is, the higher the current cost of policy implementation will be, and consequently the incentive to adopt the policy instead of waiting till later will be stronger. On the other hand, the higher the uncertainty of environment is, the stronger the irreversibility of ecological harm caused by pollutants per unit would be. Therefore, government should implement new environmental policy as early as possible in order to gain more ecological benefits.The contributions of this thesis are as follows.1. By constructing an optimal exploiture model of exhaustible resources under uncertainty, the thesis compares the different effects of fluctuations resulting from different processes. The continuous process often has one-side impact, while the discrete process usually has double-side impacts.2. By endogenous the effects of mining policies, the thesis establish a theoretical model about the management of exhaustible resources under uncertainty. The results indicate that the firm reacts negatively to the variations of favored policies, while reacts positively to the variations of unflavored policies when choosing its mining rate.3. Based on the empirical works on the time series of gold price, the author infers that the Geometric Brownian Motion with jump process should be the more appropriate function form of stochastic process.