Bankruptcy prediction has been of great interest to academics in the fields of accounting and finance for decades. Prior literatures focus mostly on investigating the covariates that lead to bankruptcy. In this thesis, however, we extend the issue of interest to what are the possible covariates that cause significant jumps in bankruptcy probability for a company. We consider the BSM-probability measure examined by Hillegeist, Keating, Cram, and Lundsedt (2004) to help us calculate the variation in bankruptcy probabilities for companies. In addition, recurrent event data analysis is applied to explore these jumps in bankruptcy intensity. By investigating the S&P500 constituents with sample consists of 343 S&P500-listed companies and 17,836 quarter observations starting from 1994 to 2007, we find that, in three of our models, all of these six covariates are negatively related to the recurrences of event that a company will suffer significant jumps in its bankruptcy probability during the next quarter. Additionally, macroeconomic covariates have greater explanatory power as factors affecting the probability of these jumps, while company-specific covariates contribute less to these recurrences of events. In comparison, we conduct another estimation based on the observation of slight increases in bankruptcy probability for companies. Contrary to what we find on the prior dataset, our empirical results suggest the factors that evoke these events are less prominent and their influences on the event recurrence are mixed.

規模效應是資本資產定價模型所無法解釋的報酬異常現象中，最常被討論的一個。本文首先將探討台灣股市是否具有規模效應情形，若有，再進一步檢視其型態為何。接下來，本文試圖了解是否公司發生財務危機的機率高低會與規模溢酬有所關連，亦即，小公司因為較容易發生財務危機事件，因此平均而言，較大公司有更高的報酬率。本研究將採用Shumway(2001)的羅吉斯迴歸模型來估算公司發生財務危機事件之機率，並且比較不同變數之預測能力如何。 經由實證結果，發現1986年至2009年的台灣股市具有規模效應情形，此結果與之前幾位研究者之研究結果相符。而在財務危機事件機率的部份，亦可看出發生財務危機機率較高的投資組合享有較高的報酬率，此情形在小市值規模的公司身上尤其明顯。從以上發現，我們可以推論財務危機風險確實為構成規模效應的因素之一。 / Size effect is one of wildly-discussed pricing anomalies that cannot be explained by capital assets pricing model, we would like to exam whether it exists in Taiwan stock markets and how its pattern is. Furthermore, we assume the higher financial distress risk a company has, the higher expected return it will earn. That is, there is positive correlation between financial distress risk and return. Following the logistic model developed by Shumway(2001), we explore the list of variables which have greater explanatory power in prediction. Through empirical data with stocks listed and ever listed on Taiwan Stock Exchange and GreTai Securities Market, we find size effect does exist. The result is consistent with previous study. We also see firms with higher distress risk tend to have higher returns, this condition is especially obvious in small companies. So we can infer that having higher distress risk is one of the reasons why small companies can earn higher returns, they are consistent with our conjecture.

動態規劃的問題並不一定都存在封閉解(closed form solution)，即使存在，其過程往往也相當繁雜。本研究擬以 Gerrard & Haberman (2004) 的模型為基礎，並使用逼近動態規劃理論解的數值方法來求解，此方法參考自黃迪揚(2009)，其研究探討在有無封閉解的動態規劃下，使用此數值方法求解可以得到 逼近解。本篇嘗試延伸其方法，針對不同類型的限制，做更多不同的變化。Gerrard & Haberman (2004)推導出退休後投資於風險性資產與無風險性資產之最適投資策略封閉解， 本研究欲將模型投資之兩資產衍生至三資產，分別投資在高風險資產、中風險資產與無風險資產，實際市場狀況下禁止買空賣空的情況與風險趨避程度限制資產投資比例所造成的影響。並探討兩資產與三資產下的投資結果，並加入不同的目標函數:使用控制變異數的限制式來降低破產機率、控制帳戶差異部位讓投資更具效率性。雖然加入這些限制式會導致目標函 數過於複雜，但是用此數值方法還是可以得出逼近解。 / Dynamic Programming’s solution is not always a closed form. If it do exist, the solution of progress may be too complicated. Our research is based on the investing model in Gerrard & Haberman (2004), using the numerical solution by Huang (2009) to solve the dynamic programming problem. In his research, he found out that whether dynamic programming problem has the closed form, using the numerical solution to solve the problems, which could get similar result. So in our research, we try to use this solution to solve more complicate problems. Gerrard & Haberman (2004) derived the closed form solution of optimal investing strategy in post retirement investment plan, investing in risky asset and riskless asset. In this research we try to invest in three assets, investing in high risk asset, middle risk asset and riskless asset. Forbidden short buying and short selling, how risk attitude affect investment behavior in risky asset and riskless asset. We also observe the numerical result of 2 asset and 3 asset, using different objective functions : using variance control to avoid ruin risk, consideration the distance between objective account and actual account to improve investment effective. Although using these restricts may increase the complication of objective functions, but we can use this numerical solution to get the approximating solution.