Open AccessTHE ROLE OF STOCHASTIC MONOTONICITY IN THE DECISION TO CONSERVE OR HARVEST OLD‐GROWTH FOREST
Author(s) -
Reed William J.,
Ye Jane J.
Publication year - 1994
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1994.tb00169.x
Subject(s) - amenity , monotonic function , geometric brownian motion , equivalence (formal languages) , ambiguity , expected value , poisson distribution , mathematical optimization , value (mathematics) , mathematical economics , brownian motion , mathematics , stochastic modelling , optimal stopping , economics , econometrics , computer science , statistics , service (business) , finance , mathematical analysis , economy , diffusion process , discrete mathematics , programming language
The problem of when, if ever, a stand of old‐growth forest should be harvested is formulated as an optimal stopping problem, and a decision rule to maximize the expected present value of amenity services plus timber benefits is found analytically. This solution can be thought of as providing the “correct” way in which cost‐benefit analysis should be carried out. Future values of amenity services provided by the standing forest and or timber are considered to be uncertain and are modeled by Geometric Poisson Jump (GPJ) processes. This specification avoids the ambiguity which arises with Geometric Brownian Motion (GBM) models, as to which form of stochastic integral (Itô or Stratonovich) should be employed, but more importantly allows for monotonic (yet stochastic) processes. It is shown that monotonicity (or lack of it) in the value of amenity services relative to timber values plays an important part in the solution. If amenity values never go down (or never go up) relative to timber values, then the certain‐equivalence cost‐benefit procedure provides the optimal solution, and there is no option value. It is only to the extent that the relative valuations can change direction that the certainty‐equivalence procedure becomes sub‐optimal and option value arises.