Optimal Stopping Problem with Offers from One of Two Possible Distributions

論文發表人: 李妍明（南加州大學工業工程系博士班）

http://meetings.informs.org/DC08/ 

 We introduce an optimal stopping problem for selling an asset when the fixed but unknown distribution of successive offers is either f₁ or f₂. The seller has to decide whether to stop or to continue after receiving an offer. A dynamic programming model and some heuristic optimal policies are presented. Using simulation, the performances of the heuristic methods are evaluated and an upper bound for the optimal expected return is derived. We then present a variant of this problem in which the seller now has to set up a reserve price before offers come in. We show that the optimal solution can be obtained by linear programming.

 

本研究主題為最適停止問題中的資產銷售問題。賣家能夠逐一觀察買家們的出價價格；當賣家拒絕某買家的出價時，必須支付一定成本才能繼續觀察下一個出價；一旦買家的出價被拒絕，賣家不能回頭再選擇將資產銷售給該買家；賣家的主要目標是尋找獲得最大利潤的最佳策略，決定何時該將資產銷售出去。於本研究中，我們假設當出價資訊不充足，僅知來自於兩個可能的機率分配之一時，賣家該如何找出最佳策略。我們應用動態規劃建構並分析數學模型，提出三個啟發式解，並運用模擬來評估啟發式解的利潤與最大利潤的關係。此外，我們亦研究此最適停止問題的變化型，將此假設應用於線上競標機制。此時賣家的決策為在觀察出價前制定銷售底價。我們運用動態規劃與線性規劃，為此問題求得最佳策略。