A 4-stated DICE: quantitatively addressing uncertainty effects in climate change

We introduce a version of the DICE-2007 model designed for uncertaintyanalysis. DICE is a wide-spread deterministic integrated assessment model of climatechange. However, climate change, long-term economic development, and theirinteractions are highly uncertain. A thorough empirical analysis of the effects ofuncertainty requires a recursive dynamic programming implementation of integratedassessment models. Such implementations are subject to the curse of dimensionality.Every increase in the dimension of the state space is paid for by a combinationof (exponentially) increasing processor time, lower quality of the value function andcontrol rules approximations, and reductions of the uncertainty domain. The paperpromotes a four stated recursive dynamic programming implementation of the DICEmodel. Our implementation solves the infinite planning horizon problem for an arbitrarytime step. Moreover, we present a closed form continuous time approximationto the exogenous (discretely and inductively defined) processes in DICE and presenta Bellman equation for DICE that disentangles risk attitude from the propensity tosmooth consumption over time.