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mean-variance hedging for Pricing European-type Contingent Claims with Transaction Costs

Acta Mathematica Sinica,English Series 2003年第4期19卷 655-670页

作者： DaoBaiLIU InstituteofMathematics FudanUniversityShanghai200433P.R.China

In this paper, a European-type contingent claim pricing problem withtransaction costs is considered by a mean-variance hedging argument. The investor has to paytransaction costs which are proportional to the amount of stock transacted. The writer's hedgingobject is to minimize the hedging risk, defined as the variance of hedging error at expiration, witha proper expected excess return level. At first, we consider the mean-variance hedging problem: forinitial hedging wealth f, maximizing the excess expected return under the minimum hedging risklevel V_0. On the other hand, we consider a mean-variance portfolio problem, which is to maximizethe expected return with initial wealth 0 under the same risk level V_0. The minimum initial hedgingwealth f, which can offset the difference of the maximum expected return of these two problems, isthe writer's price.

关键词： contingent claim pricing mean-variance hedging transaction costs stochastic control viscosity solution

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mean-variance hedging for General Claims in an Incomplete Market: Numeraire Method

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Journal of Shanghai Jiaotong university(Science) 2003年第2期8卷 175-178页

作者：王桂兰叶中行 Dept. of Mathematics Shanghai Jiaotong Univ. Shanghai 200030 China

This paper considered the problem of hedging a European call (put) option for a diffusion model where the asset price is influenced by n uncertain factors. The market is thus incomplete implying that perfect hedging is not possible. To derive a hedging strategy, it follows the approach based on the idea of hedging under a mean-variance criterion suggested by Schweizer. A very simple solution of this hedging problem by using the numeraire method was presented and some examples with explicit solutions were given.

关键词： mean-variance hedging incomplete market numeraire European options

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mean-variance hedging for Pricing Contingent Claims with Transaction Costs

Mean-Variance Hedging for Pricing Contingent Claims with Tra...

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第二十届中国控制会议

作者： Daobai Liu Institute of Mathematics, Fudan University, Shanghai 200433, China

In this paper, a European type contingent claim pricing problem, with transaction costs is considered by mean-variance hedging argument. The investor has to pay transaction costs which is proportional to the amount of stock transacted. The writer’s hedging object is to minimize the hedging risk, defined as the variance of hedging error at expiration, with proper expected excess return level. Then the writer’s price of contingent claim is given.

关键词： contingent claim pricing mean-variance hedging transaction costs.

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