Wealth Management and Uncertain Tipping Points

Abstract

We analyze optimal wealth management, within a global setting, where accumulation of GHGs caused by extraction of fossil resources affects the probability distribution for hitting a threshold or tipping point, indicating a climate change. We derive an optimal strategy for overall wealth management, within a Ramsey-Hotelling-framework. We have two assets; one being reproducible (reversible capital equipment) and another being non-reproducible (stock of exhaustible natural resources – fossil fuels). Resources, along with capital equipment, are inputs in the production of an aggregate output allocated to consumption and net investment. Resource extraction adds to a stock of GHGs that affects the likelihood for a catastrophic event. If, and when, such an event occurs there is a downscaling of production opportunities. We derive a first-best precautionary global tax on using fossil fuel, which internalizes the present value of (conditional) expected welfare loss of hitting a threshold, as well as a set of risk-modified optimality conditions for overall wealth management, as long as no catastrophe has occurred.

Keywords: wealth management, stochastic tipping points, catastrophic outcome, precautionary taxation, social rates of discount

JEL Classification: E210, O440, Q320