Markowitz's portfolio optimization in an incomplete market

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	Markowitz's portfolio optimization in an incomplete market
	Xia, JM; Yan, JA
	2006
发表期刊	MATHEMATICAL FINANCE
ISSN	0960-1627
卷号	16 期号:1 页码:203-216
摘要	In this paper, for a process S, we establish a duality relation between K-p, the L-p(P)-closure of the space of claims in L-p(P), which are attainable by "simple" strategies, and M-q,M-s, all signed martingale measures Q with (dQ)/(dP) is an element of L-q(p), where p >= 1, q >= 1 1 and (1)/(p) + (1)/(q) = 1. If there exists a Q is an element of M-q,M-s with (dQ)/(dP) > 0 a.s., then K-p consists precisely of the random variables integral(0)(T) theta dS such that theta is predictable S-integrable and dE[dQ/dP integral(0)(T) theta dS] = 0 for all Q is an element of M-q,M-s. The duality relation corresponding to the case p = q = 2 is used to investigate the Markowitz's problem of mean-variance portfolio optimization in an incomplete market of semimartingale model via martingale/convex duality method. The duality relationship between the mean-variance efficient portfolios and the variance-optimal signed martingale measure (VSMM) is established. It turns out that the so-called market price of risk is just the standard deviation of the VSMM. An illustrative example of application to a geometric Levy processes model is also given.
关键词	mean-variance portfolios convex duality signed martingale measures attainable claims Levy processes
语种	英语
WOS研究方向	Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences
WOS类目	Business, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods
WOS记录号	WOS:000235136300012
出版者	BLACKWELL PUBLISHING
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2992
专题	应用数学研究所
通讯作者	Yan, JA
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Ctr Financial Engn & Risk Management, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Xia, JM,Yan, JA. Markowitz's portfolio optimization in an incomplete market[J]. MATHEMATICAL FINANCE,2006,16(1):203-216.
APA	Xia, JM,&Yan, JA.(2006).Markowitz's portfolio optimization in an incomplete market.MATHEMATICAL FINANCE,16(1),203-216.
MLA	Xia, JM,et al."Markowitz's portfolio optimization in an incomplete market".MATHEMATICAL FINANCE 16.1(2006):203-216.