本論文探討平均成本法與平均價值法。我們以內部報酬率作為比較兩投資策略之指標。假設股價為幾何布朗運動下使用蒙地卡羅模擬法，探討平均成本法與平均價值法在不同價格波動率、投資時間、每期投資額變化率以及市場趨勢下，績效是否有明顯差異，並比較模擬與台股實證結果。模擬結果顯示，當市價波動率大時，長期投資下平均價值法將明顯優於平均成本法。而模擬與實證結果均顯示，若每期投資額降低，則平均價值法表現越優於平均成本法，而平均價值法之內部報酬率與風險均高於平均成本法。但平均價值法之單位預期報酬下所承擔之風險小於平均成本法。

This thesis studies the dollar-cost averaging and the value averaging. We use the internal rate of return to compare these two investment strategies. Assuming a geometric Brownian motion for stock prices, we use Monte Carlo technique to study the dollar-cost averaging and the value averaging under various settings of market price volatilities, investment time horizons, amount change , and market trend. A comparison of the results on Monte Carlo simulation and empirical Taiwan stock index was made. Simulation dictates that with larger price volatility, the value averaging will be better than the dollar-cost averaging under longer investment time horizon. . Both simulation and empirical study show that , by decreasing investment amount of each period, the internal rate of return and risk of the value averaging are higher than those of the dollar-cost averaging. But the risk borne by the unit expected return of the value averaging is less than that of the dollar-cost averaging.

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