在線性累積前景理論下最佳投資策略的選擇

Abstract

本論文我們關心的是『如何投資在股票市場將使我們獲利最大』，此問題針對於某些投資者在面對不確定的決策行為符合Linear Cumulative Prospect Theory(線性累積前景理論, LCPT)。LCPT 為Cumulative Prospect Theory 的一特例。本論文採用連續型Black-Scholes 金融市場模型含有一股票和一銀行帳戶。我們推導出其最大獲利的總資產是由投資者的probability weighting function (決策權數函數) 和 discounted Radon-Nikodym derivative 共同決定。在本論文的最後，我們給一例子算出其最大獲利，而且觀察當我們改變其參數時其最大獲利的變化。

In this thesis we are concerned with the optimal portfolio selection for an investor who makes decision according to the Linear Cumulative Prospect Theory (LCPT). LCPT is a special case of Cumulative Prospect Theory. We investigate the case of a continuous-time economy model with one risk-free asset and one risky asset. The maximum value of terminal wealth is a supremum relative to the probability weighting function and the discounted Radon-Nikodym derivative. We derive some numerical results and illustrate how these parameters afects the maximum value.