Mean-Variance Hedging
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Author / Producer
Date
2010
Publication Type
Encyclopedia Entry
ETH Bibliography
yes
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Abstract
Suppose discounted asset prices in a financial market are given by aP‐semimartingaleS. Mean–variance hedging is the problem of approximating, with minimal mean‐squared error, a given payoff by the final value of a self‐financing trading strategy. Mean–variance portfolio selection consists of finding a self‐financing strategy whose final value has maximal mean and minimal variance. In both cases, this leads to projecting a random variable inL²(P) onto a space of stochastic integrals ofS, and, apart from proving closedness of that space, the main difficulty is to find more explicit descriptions of the optimal integrand. Both problems have a wide range of applications, and many examples and solution techniques can be found in the literature. Nevertheless, challenging open questions still remain.
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Publication status
published
Editor
Book title
Encyclopedia of Quantitative Finance
Journal / series
Volume
3
Pages / Article No.
1177 - 1181
Publisher
Wiley
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Hedging; Portfolio choice; Quadratic criterion; Variance-optimal martingale measure; Mean-variance trade-off; Linear-quadratic stochastic control; Backward stochastic differential equations
Organisational unit
03658 - Schweizer, Martin / Schweizer, Martin