MARKOWITZ'S PORTFOLIO OPTIMIZATION IN AN INCOMPLETE MARKET |
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Authors: | Jianming Xia Jia-An Yan |
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Institution: | Center for Financial Engineering and Risk Management, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China |
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Abstract: | In this paper, for a process S , we establish a duality relation between Kp , the - closure of the space of claims in , which are attainable by "simple" strategies, and , all signed martingale measures with , where p ≥ 1, q ≥ 1 and . If there exists a with a.s., then Kp consists precisely of the random variables such that ? is predictable S -integrable and for all . 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 Lévy processes model is also given. |
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Keywords: | mean–variance portfolios convex duality signed martingale measures attainable claims Lévy processes |
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