The optimal harvesting problem under risk aversion ∗

We study the exploitation of a one species forest plantation when timber price is uncertain. The work focuses on providing optimality conditions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We use risk averse stochastic dynamic programming and use the Conditional Value-at-Risk (CVaR) as our main risk measure. We consider two important cases: when prices follow a geometric Brownian motion we completely characterize the optimal policy for all possible choices of drift and discount factor. When prices are governed by a mean-reverting (Ornstein-Uhlenbeck) process we provide sufficient conditions, based on explicit expressions for a reservation price period above which harvesting everything available is optimal. In both cases we solve the problem for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state. We compare our results with the risk neutral framework and highlight the differences between the two cases. We generalize our results to any coherent risk measure that is affine on the current price and calculate the coefficients for risk measures other than the CVaR.