Estimating the spatial amplification of damage caused by degradation in the Amazon.

The Amazon rainforests have been undergoing unprecedented levels of human-induced disturbances. In addition to local impacts, such changes are likely to cascade following the eastern-western atmospheric flow generated by trade winds. We propose a model of spatial and temporal interactions created by this flow to estimate the spread of effects from local disturbances to downwind locations along atmospheric trajectories. The spatial component captures cascading effects propagated by neighboring regions, while the temporal component captures the persistence of local disturbances. Importantly, all these network effects can be described by a single matrix, acting as a spatial multiplier that amplifies local forest disturbances. This matrix holds practical implications for policymakers as they can use it to easily map where the damage of an initial forest disturbance is amplified and propagated to. We identify regions that are likely to cause the largest impact throughout the basin and those that are the most vulnerable to shocks caused by remote deforestation. On average, the presence of cascading effects mediated by winds in the Amazon doubles the impact of an initial damage. However, there is heterogeneity in this impact. While damage in some regions does not propagate, in others, amplification can reach 250%. Since we only account for spillovers mediated by winds, our multiplier of 2 should be seen as a lower bound.

A non-local free boundary problem arising in a theory of financial bubbles.

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is [Formula: see text] and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero.

Recursive utility in a Markov environment with stochastic growth.

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.