風險改變與對應決策:理論、方法與應用

Abstract

本博士論文由三篇文章合併而成；它們所研究的主題都是風險改變之下，對應決策的改變。 假想一個決策者付出努力以達成目標。他面臨兩種風險，其一是失敗的風險；其二是初始環境與目標環境改變的風險。第一篇文章研究當初始環境或是目標環境改變時，這個決策者應如何調整他的最適努力程度。 Gollier (1995, JET) 所提出的中央優越 (central dominance) 是個與隨機優越(stochastic dominance) 不同的重要概念。當風險改變時，中央優越可以告訴我們一個決策者是否應該增加或減少他的決策變數，但隨機優越並不能告訴我們相同的結論。在第二篇文章裡，我們提出了第一個中央優越的檢定，它可以看作是一個函數不等式的檢定。我們推導出檢定統計量的分配下界，並提出計算臨界值的方法。另外我們也模擬了這個檢定在不同樣本數下的表現，並將它應用在加拿大的所得分配資料上。我們發現加拿大的所得分配在不同年度之間有中央優越的關係，並得出有趣的政策應用。 在第三篇文章裡，我們提出了一個計算風險指標的方法，用來計算Aumann與Serrano(2008)以及Huang, Tzeng, Wang(2012)所提出的風險指標。這個方法可以利用一到四階動差的資訊，並且計算上相當方便。我們發現Huang, Tzeng, Wang(2012)所提出的風險指標在簡單的投資組合模型中，是投資者決定投資金額的充分統計量。於是我們根據這個性質，建構了一個交易策略。我們的實證結果發現，在我們的資料期間裡，這個交易策略能夠勝過所有”買了以後放著不再交易”的交易策略。

The dissertation contains three articles. All of them focus on investigating change in decision resulted from change in risk. When decision makers invest in effort to reach their targets, they face multiple sources of risk: first the risk of failure and second the noise that surrounds either the target or the initial situation. In the first article, we examine how effort is adjusted to account for changes in this risky environment. Central dominance (CD) introduced in Gollier (1995, Journal of Economic Theory) is a risk concept that differs from stochastic dominance in an important way. In particular, CD implies a deterministic comparative statics of change in decision when risk changes, but SD does not have such implication. In the second article, we propose the first test of central dominance, which amounts to checking a functional inequality. We derive the asymptotic distribution of a lower bound of the proposed test and suggest a bootstrap procedure to compute the critical values. We also conduct simulations to evaluate the performance of this test. Our empirical study finds CD relations among Canadian family income distributions in different years and results in interesting policy implications. In the third article, we propose a method to calculate risk measures proposed by Aumann and Serrano (2008) and Huang et al. (2012). This method utilizes information about mean, variance, skewness, and kurtosis of a distribution. We find that the risk measure in Huang et al. (2012) is sufficient information for investment decision in a simple portfolio selection model, and therefore we construct a trading strategy with respect to the measure. Our empirical results show that this trading strategy outperforms any buy-and-hold trading strategies during sample period from January 2001 to October 2009.