| Abstract: | This paper extends the one-state-variable stochastic tree problem to the two-state-variable case. (Considering, for example, a tree whose size and price evolve according to two different Wiener processes, we solve for the optimal cutting time. The optimization of the expected present discounted value of the tree is converted to a standard free-boundary problem. Analytical results are reported. In particular we find that more variance near the optimal free boundary will increase the value of the tree. Finally, a method is developed to find the numerical solution to the free boundary problem. A numerical example is presented. |
