不完全市場之下或有請求權評價之研究

Three Essays on Contingent Claim Valuation in Incomplete Markets

蔡宏洲(Hung-Chou Tsai)

指導教授 ： 李存修

共同指導教授 ： 何淮中

國立臺灣大學/管理學院/財務金融學研究所/博士(2007年)

https://doi.org/10.6342/NTU.2007.10065

摘要

無資料

關鍵字

效用無差異價格 ； 跳躍-擴散模型 ； 平賭

並列摘要

The main purpose of this dissertation is to investigate the problems of contingent claim valuation in incomplete markets, especially focused on the pricing measures for Levy processes. This dissertation is constituted by three essays and each essay is self-contained.

Essay 1 reviews some known results in an incomplete market in the case of exponential utility function. We also discuss the notion of utility indifference price for a contingent claim and investigate the asymptotic behavior of utility indifference price.

Essay 2 uses the Esscher transform to construct a martingale measure in the framework of geometric Levy process. By means of a relation between exponential Levy process and stochastic exponential of Levy process, we have shown that a Levy process is a martingale if and only if its stochastic exponential is a martingale. Using this result, we also define a necessary condition for the Esscher measure to be the minimal entropy martingale measure.

Essay 3 formulates an approach to computing the density process of the minimal entropy martingale measure for a jump-diffusion model and the stochastic volatility model by Barndorff-Nielsen and Shepherd. In addition, we also calculate the explicit forms of the minimal entropy martingale measure for those two models.

並列關鍵字

Esscher measure ； jump-diffusion model ； Levy process ； minimal entropy martingale measure ； utility indifference price

參考文獻

1.Becherer, D. (2003) Rational hedging and valuation of integrated risks under constant absolute risk aversion, Insurance: Mathematics and Economics 33, 1-28.

2.Csiszar, I. (1975) I-divergence geometry of probability distributions and minimization problems, Annals of Probability 3, 146-148.

5.Frittelli, M. (2000) The minimal entropy martingale measure and the valuation problem in incomplete markets, Mathematical Finance 10, 39-52.

6.Fujiwara, T., Miyahara, Y. (2003) The minimal entropy martingale measures for geometric Levy processes, Finance and Stochastics 7, 509-531.

7.Henderson, V., Hobson, D. (2004) Utility indifference pricing: An overview, Preprint.