The stochastic Mitra–Wan forestry model: risk neutral and risk averse cases

Abstract

We extend the classic Mitra and Wan forestry model by assuming that prices follow a geometric Brownian motion. We move one step further in the model with stochastic prices and include risk aversion in the objective function. We prove that, as in the deterministic case, the optimal program is periodic both in the risk neutral and risk averse frameworks, when the benefit function is linear. We find the optimal rotation ages in both stochastic cases and show that they may differ significantly from the deterministic rotation age. In addition, we show how the drift of the price process affects the optimal rotation age and how the degree of risk aversion shortens it. We illustrate our findings for an example of a biomass function and for different values of the model's parameters.

On the Mitra–Wan forest management problem in continuous time

“…Finally we define the cut-off function ψ ∈ C ∞ ([0, S]; R + ) such that for fixed s, s 1 , s 2 , with 0 <s < s 1 < s 2 < S, ψ ≡ 1 on [0, s 1 ], ψ ≡ 0 on [s 2 , S], ψ decreasing on [s 1 , s 2 ]. 3 As pointed out to us by a referee, a monotonicy results for the Faustmann cutting age in discrete time is reported in a forthcoming paper (see Piazza and Pagnoncelli [38]). …”

“…The proof follows from Lemma A.6 using density of step-functions approximating g and satisfying (38). 2…”