The optimal harvesting problem under price uncertainty: the risk averse case
We study the exploitation of a one species, multiple stand forest plantation when timber price is governed by a stochastic process. Our model is a stochastic dynamic program with a weighted mean-risk objective function, and our main risk measure is the Conditional Value-at-Risk. We consider two stochastic processes, geometric Brownian motion and Ornstein–Uhlenbeck: in the first case, we completely characterize the optimal policy for all possible choices of the parameters while in the second, we provide sufficient conditions assuring that harvesting everything available is optimal. In both cases we solve the problem theoretically for every initial condition. We compare our results with the risk neutral framework and generalize our findings to any coherent risk measure that is affine on the current price.
KeywordsMultistage stochastic programming Optimal harvesting Forestry Coherent risk measures
This research was partially supported by Programa Basal PFB 03, CMM. B.K. Pagnoncelli acknowledges the financial support of FONDECYT under projects 11130056 and 1120244. A. Piazza acknowledges the financial support of FONDECYT under Project 11090254 and of CONICYT Anillo ACT1106 and CONICYT REDES 140183.
- Boychuk, D., & Martell, D. (1996). A multistage stochastic programming model for sustainable forest-level timber supply under risk of fire. Forest Science, 42(1), 10–26.Google Scholar
- Brazee, R., & Mendelsohn, R. (1988). Timber harvesting with fluctuating prices. Forest Science, 34(2), 359–372.Google Scholar
- Dixit, A., & Pindyck, R. (1994). Investment under uncertainty. Princeton: Princeton University Press.Google Scholar
- Gong, P. (1998). Risk preferences and adaptive harvest policies for even-aged stand management. Forest Science, 44(4), 496–506.Google Scholar
- Gong, P., & Löfgren, K. (2003). Risk-aversion and the short-run supply of timber. Forest Science, 49(5), 647–656.Google Scholar
- Lembersky, M., & Johnson, K. (1975). Optimal policies for managed stands: An infinite horizon Markov decision process approach. Forest Science, 21(2), 109–122.Google Scholar
- Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.Google Scholar
- Piazza, A., & Pagnoncelli, B. (2014). The optimal harvesting problem with price uncertainty. Annals of Operations Research, 217(1), 425–445.Google Scholar
- Piazza, A., & Pagnoncelli, B. K. (2015). The stochastic mitra-wan forestry model: Risk neutral and risk averse cases. Journal of Economics, 115, 175–194.Google Scholar
- Plantinga, A. (1998). The optimal timber rotation: An option value approach. Forest Science, 44(2), 192–202.Google Scholar
- Zhong-wei, W., & Yan, P. (2009) Measurement of forest fire risk based on var. In International conference on management science and engineering, 2009. ICMSE 2009. IEEE.Google Scholar