Endogenous Risks and Learning in Climate Change Decision Analysis

We analyze the effects of risks and learning on climate change decisions. A two-stage, dynamic, climate change stabilization problem is formulated. The explicit incorporation of ex-post learning induces risk aversion among ex-ante decisions, which is characterized in linear models by VaR- and CVaR-type risk measures. Combined with explicit introduction of "safety" constraints, it creates a "hit-or-miss" type decision-making situation and shows that, even in linear models, learning may lead to either less-or more restrictive ex-ante emission reductions. We analyze stylized elements of the model in order to identify the key factors driving outcomes, in particular, the critical role of quantiles of probability distributions characterizing key uncertainties

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199