On a multidimensional oil exploration problem

[摘要] This paper is concerned with optimal strategies for drilling in anoil exploration model. An exploration area containsn1large andn2small oilfields, wheren1andn2are unknown, andrepresented by a two-dimensional prior distributionπ. A single exploration well discovers at mostone oilfield, and the discovery process is governed by someprobabilistic law. Drilling a single well costsc, and the values of a large and small oilfield arev1andv2respectively,v1>v2>c>0. At each timet=1,2,…, the operator is faced with the option of stopping drilling andretiring with no reward, or continuing drilling. In the event ofdrilling, the operator has to choose the numberk,0≤k≤m(mfixed), of wells to be drilled. Rewards are additiveand discounted geometrically. Based on the entire history of theprocess and potentially on future prospects, the operator seeksthe optimal strategy for drilling that maximizes the totalexpected return over the infinite horizon. We show that whenπ≻π′in monotone likelihood ratio,then the optimal expected return under priorπis greater than or equal to the optimal expected return underπ′. Finally, special cases where explicitcalculations can be done are presented.

[学科分类] 应用数学