13 August 2007
Essays on Optimal Stopping and Control of Markov Processes by Jukka Lempa, M.A., shall be examined within the context of quantitative methods in the economic sciences as an academic subject, at Turku School of Economics, Saturday, 18 Aug. 2007.
Jukka Lempa’s doctoral thesis is particular to the field of applied mathematics. The object of research is a broad class of stochastic control theory models. In these models, the goal is to steer the course of the random, i.e., stochastic process in an optimal manner. The models are built from three components: the stochastic process that is the object of control, the steering or control process, and the reward function.
At each moment, the controller of a random process in the model has two possibilities at his/her disposal. S/he may allow the process to ’live freely’ or, alternatively, steer the course of the process by exercising control. In exercising control, the controller always obtains the input specified by the reward function. The goal is to optimally steer the process in such a manner that the anticipated current value of reward or compensation obtained from such control would be maximal.
Innumerable practical applications can be found for the control of random processes. Consider a situation where a private small-sized forest owner should specify what sorts of fellings s/he would consider worth carrying out in the commercial forest s/he owns. In commerce that deals with sawtimber trees, the generally utilized form of trade is the standing sale of timber, in which the owner sells the right to felling from his/her forest to, e.g., a large forestry enterprise. In this respect, the forest owner should actually decide him/herself when s/he will sell the right to fellings, and which sort of right to felling this concerns.
In this situation, the condition of the random process being controlled depicts the overall stump value of the sawtimber tree at each moment. The sawtimber tree stump price is affected by market-derived factors such as the demand for pulpwood or sudden changes in supply, as well as the biological factors affecting the growth of the wood, such as changes in the prevailing weather or unanticipated epidemics of disease. Because the impacts of these sorts of factors on the stump price are not entirely anticipated, modelling based on fluctuations in the timber stump price should include the random element model.
The above-mentioned control currently corresponds to the felling strategy formulated on the basis of sold felling rights: in other words, a plan based on when the wood is to be felled, and how much. Conversely, a single instance of reward or compensation corresponds to the income specified by the stump price for individual fellings. Taking into account the randomness of stump prices as well as the slowness of forest renewal, it is worthwhile for the forest owner under these circumstances to sell the felling rights in such a manner that the current value of the overall income received for the fellings is maximized.
The doctoral thesis can be read at:
http://info.tse.fi/julkaisut/vk/Ae8_2007.pdf
Additional information:
Jukka Lempa
+358 2 481 4314
jukka.lempa(a)tse.fi