曾郁仁臺灣大學:財務金融學研究所利政洋Lih, Jeng-YangJeng-YangLih2010-05-112018-07-092010-05-112018-07-092009U0001-2606200919534000http://ntur.lib.ntu.edu.tw//handle/246246/182861本研究利用中國信託、台北富邦銀行每期「期望報酬」、「頭獎累積獎金」與「銷售量」進行迴歸分析。然後再以求出之迴歸模型推廣至不同球數下之銷售量預測，並加入成本損益之考量發現在何種球數時銷售量可以達到最大，而使發行公司能獲利最多。固定獎金發放額度下，不論是中國信託、台北富邦銀行、或是兩家合併後的數據，欲達到最大銷售量最適球數約為35~36顆。在不固定獎金發放額度下，以可發放獎金的改變、陸獎與普獎獎金的改變、頭獎獎金的改變分別進行觀察。一，當可發放獎金占所有獎金比例愈高時，估計銷售量與最適球數均呈現下降的趨勢。二，當陸獎與普獎獎金愈高時，估計銷售量呈現下降的趨勢，但最適球數只有當固定獎金大於現行固定獎金時呈現上升趨勢，反之則沒有任何變動。三，當頭獎獎金比例占可發放獎金愈高時，估計銷售量呈現下降的趨勢，但最適球數不管頭獎獎金比例均維持在35~36顆。研究最後以最新發行的威力彩為研究對象，以在樂透彩中建立的模型去估計其銷售量與球數的關係，發現現行的威力彩欲達到最高銷售量，其最適球數為20顆。This paper extracts expected value, accumulated first prize money and sales from Chinatrust and Taipei Fubon lottery database to run a simple regression. This paper then adds in cost concerns and uses the regression results to predict expected sales under different number of balls while concluding the optimal number of balls a lottery company should play with if it aims to maximize its profits. nder current prize money distribution, the number of balls for Chinatrust, Taipei Fubon, and the mixture of two companies to maximize profits all points to 35 or 36. If the current prize money distribution is changed, this paper views the changes in three aspects, which are the change of distributable prize money, change of sixth prize and seventh prize money and the change of first prize money. For one, this paper found out when the amount of distributable money increased, expected sales and number of balls both decreased. Secondly, the higher the sixth and seventh prize money amount were the lower it was for expected sales while the number of balls rose only when the prize money were higher than before. Thirdly, when first prize money accounted for a bigger portion in distributable prize money, expected sales declined but the number of balls remained at 35 or 36. s for the new super lotto, based on the model conducted this paper concludes for super lotto to maximize its profits it needs to change its number of balls to 20.目錄錄 i目錄 ii目錄 ii要 1bstract 2一章 序論 4一節 研究目的 4二節 研究方法 4二章 文獻探討 6三章 大樂透規則與各獎項之中獎機率 8一節 大樂透規則 8二節 購買一張樂透彩之期望值 9三節 獎金分配規則 9四節 各獎項期望值之計算 10四章 預測不同球數之樂透彩銷售量 13一節 迴歸分析 13二節 不同球數下之估計銷售量 14五章 獎金發放額度的改變 26一節 可發放獎金的改變 26二節 陸獎和普獎之改變 28三節 頭獎獎金之改變 30六章 威力彩最適球數之探討 32一節 威力彩規則 32二節 購買一張威力彩彩券之期望值 33三節 獎金分配規則 33四節 各獎項期望值之計算 34五節 迴歸分析 37六節 不同球數下之估計銷售量 38七章 結語與建議 39考文獻 40application/pdf1776034 bytesapplication/pdfen-US樂透彩偏態期望報酬LotterySkewnessExpected Valuethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/182861/1/ntu-98-R96723032-1.pdf