Carbon markets, like other commodity markets, are volatile. They react to stochastic "disequilibrium" spot prices, which may be affected by inadequate policies, speculations and bubbles. The market-based emission trading, therefore, does not necessarily minimize abatement costs and  achieve emission reduction goals. We introduce a basic stochastic model integrating emissions reduction, monitoring and trading costs allowing us to analyze the robustness of emission and uncertainty reduction policies under environmental safety constraints asymmetric information and  other multiple anthropogenic and natural uncertainties. Explicit treatment of uncertainties provides incentives for reducing them before trading. We illustrate functioning of the robust market with numerical results involving such countries as the US, Australia, Canada, Japan, EU27, Russia,  Ukraine. In particular, we analyze if the knowledge about uncertainties may affect portfolios of technological and trade policies or structure of the market and how uncertainty characteristics may affect market prices and change the market structure.