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| Title: | 效用無差異價格於不完全市場下之應用
Utility indifference pricing in incomplete markets |
| Authors: | 胡介國
Hu,Chieh Kuo |
| Contributors: | 胡聯國
Hu,Len Kuo
胡介國
Hu,Chieh Kuo |
| Keywords: | 不完全市場
局部積率平賭
效用無差異定價
incomplete markets
local martingale
utility indifference pricing |
| Date: | 2009 |
| Issue Date: | 2011-10-11 19:03:53 (UTC+8) |
| Abstract: | 在不完全市場下，衍生性金融商品可利用上套利和下套利價格來訂出價格區間。我們運用效用無差異定價於此篇論文中，此定價方式為尋找一個初始交易價，會使在起始時交易商品和無交易商品於商品到期日之最大期望效用相等。利用主要的對偶結果，我們證明在指數效用函數下，效用無差異定價區間會比上套利和下套利定價區間小。
In incomplete markets, prices of a contingent claim can be obtained between the upper and lower hedging prices. In this thesis, we will use utility indifference pricing to nd an initial payment for which the maximal expected utility of trading the claim is indi erent to the maximal
expected utility of no trading. From the central duality result, we show that the gap between the seller`s and the buyer`s utility indi erence prices is always smaller than the gap between the upper and lower hedging prices under the exponential utility function. |
| Reference: | [1] Delbaen, F., P. Grandits, T. Rheinlander, D. Samperi, M. Schweizer, and C. Stricker (2002): Exponential hedging and entropic penalties, Math. Finance 12, 99-123.
[2] Follmer, H., and A. Schied (2002): Convex Measures of Risk and Trading Constraints, Finance Stochast. 6, 429-447.
[3] Fritelli, M. (2002a): The minimal Entropy Martingale Measure and the Valuation Problem in Incomplete markets, Math. Finance 10, 39-52.
[4] Grandits, P., and T. Rheinlander (1999): On the Minimal Entropy Martingale Measure, Preprint, Technical University of Berlin, to appear in Annals
of Probability.
[5] Hodges, S. D., and A. Neuberger (1989): Optimal replication of contingent claims under transaction costs, Rev. Future Markets 8, 222-239.
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[7] Kabanov, Y. M., and C. Stricker (2002): On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper, Math. Finance 12, 125-134.
[8] Kramkrov, D. O. (1996): Optimal decomposition of supermartingales and hedging of contingent claims in incomplete security markets. Probab. Theory
and Relat. Fields 105, 459-479.
[9] Kunita, H. (2004): Representation of Martingales with Jumps and Application to Mathematical Finance, Advanced Studies in Pure Mathematics, Math. Soc. Japan, Tokyo, 41, 209-232.
[10] ksendal, B.: Stochastic Di erential Equations: an introduction with applications, 6ed, Springer 2003.
[11] ksendal, B., and A. Sulem (2009): Risk indi erence pricing in jump di usion markets, Math. Finance 19, 619-637. |
| Description: | 碩士
國立政治大學
應用數學研究所
96751005
98 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0096751005 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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