投資型保單在台灣上市以來，已經經過了將近十年的時間，自從2002 年投資型保單的銷
售量有所斬獲之後，國內的保險公司也紛紛投入投資型保單的戰場。投資型保單，要保人期望
能夠享受到傳統壽險的死亡保障，同時兼具投資獲利的功能。因為保費的投資連結投資標的以
基金為主，如何作基金的配置就成了要保人所關心的課題。本研究主要針對共同基金報酬率建
立樹狀模型，在設定報酬率的期望值之下，尋求使其滿足變異數為最小的投資組合。
本研究的基金資料是自2007 年9 月到2008 年11 月總共15 個月的日價格資料。我們利
用前面12 個月的資料建立初始模型，再利用EWMA 法更新樹狀模型的各項參數(報酬率與漲
跌等機率)，探討最佳化投資策略。文中將基金分為三大類型：股票型、平衡型、債券型，分別
討論相同類型與不同類型的組合，研究兩基金組合的最佳投資比例，並用此投資比例計算投資
組合的實際報酬率。研究結果顯示，實務中此投資策略的報酬率接近設定的期望報酬率。

Investment-linked insurance in Taiwan has been listed for almost a decade since 2001.
In 2002, after the big sales of the investment-linked insurance, the domestic insurance
companies also joined the market. For the investment-linked insurance, the policyholders
retain the protection of the life insurance as well as share the earnings of the investment.
Since the main investment instruments of the investment-linked insurance are mutual funds,
it is important to study how to optimally allocate the portfolio. This research consider the
returns of the mutual funds under tree models assumption. The objective is to find the
optimal portfolio which has minimum variance and attained a given expected return level.
The problem is also known as mean-variance portfolio problem.
In the empirical work, we study eleven daily mutual fund price data from Sep. 2007
to Nov. 2008. Using the data of the first 12 months, we first establish initial tree price
models, then update the parameters of the tree model by the EWMAmethod. The optimal
trading strategies of the mean-variance portfolio are investigated under this model setting.
We class the mutual funds into three categories: equity funds, balanced funds and bond
funds. Different combination of these three kinds of funds are considered to find the
optimal trading strategy respectively. The results showed that the realized returns using
this optimal trading strategy in practice is close to the pre-specified expected return level.

1 投資型保險介紹 . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . 1
1.1 歷史與發展. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . 1
1.2 特色. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 保費運作. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 模型假設 . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . 4
2.1 風險中立機率測度(Risk Neutral Probability Measure) . . . . . . . . . . . .. . . . . . . . .. 5
2.2 效用與市場假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 最小變異投資問題(Mean-Variance Portfolio) . . . . . . . . . . . . . . . . . . 8
2.4 對數效用期望值最大問題. . . . . . . . . . . . . .. . . . . . . 11
3 資料與模型 . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . .13
3.1 資料介紹與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 建立市場模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 實證結果 . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . 19
4.1 最小變異問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 對數效用期望值最大問題. . . . . . . . . . . . . . . . . . . . 21
5 結論與建議 . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . 21

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