Abstract: Facing the objective situation that the price of emission permits is uncertain, the firm’s random profit function under a stochastic emission permits price is firstly developed, by extracting the correlations between emission permits price and rational firm’s optimal decision-making behavior, including product output, emission reduction and permits trading. Based on the criterion of conditional value-at-risk (CVaR), the analytic expression of value-at-risk (VaR) of firm’s random profit at any given confidence level is derived directly, and the CVaR model with different firm’s expected price of emission permits and confidence level is established consequently. With the goal of maximizing the CVaR of firm’s random profit, the optimal decision and its characteristics are demonstrated under the given condition level. Additionally, the influences of external scenario factors on the optimal decision and optimization result are emphatically analyzed. The results show that, the measure formula of CVaR of random profit varies between the circumstances of firm selling emission permits and purchasing emission permits duo to the difference of the emission permits price range where the profit downside risk exists under each circumstance. The optimal decision considering decision risk based on CVaR criterion would be influenced by the confidence level of decision-maker, initial quota of emission permits, the mean and standard deviation of the emission permits price, hence would systematically deviate from the risk neutral optimal decision and behave with the characteristics of risk aversion. Finally, the conclusion is verified comprehensively through numerical examples, which further indicate that the model proposed can better characterize and reflect the risk and actual behavior of firms under emission trading regulation with stochastic emission permits price.

Key words: emissions trading; stochastic emission permits price; production decision; conditional value-at-risk; risk aversion