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From bounds on optimal growth towards a theory of good-deal hedging

Please always quote using this URN:urn:nbn:de:0296-matheon-6305
  • Good-deal bounds have been introduced as a way to obtain valuation bounds for derivative assets which are tighter than the arbitrage bounds. This is achieved by ruling out not only those prices that violate no-arbitrage restrictions but also trading opportunities that are `too good'. We study dynamic good-deal valuation bounds that are derived from bounds on optimal expected growth rates. This leads naturally to restrictions on the set of pricing measure which are local in time, thereby inducing good dynamic properties for the good-deal valuation bounds. We study good-deal bounds by duality arguments in a general semimartingale setting. In a Wiener space setting where asset prices evolve as It\^o-processes, good-deal bounds are then conveniently described by backward SDEs. We show how the good-deal bounds arise as the value function for an optimal control problem, where a dynamic coherent a priori risk measure is minimized by the choice of a suitable hedging strategy. This demonstrates how the theory of no-good-deal valuations can be associated to an established concept of dynamic hedging in continuous time.

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Metadaten
Author:Dirk Becherer
URN:urn:nbn:de:0296-matheon-6305
Referee:Peter Imkeller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/07/22
Release Date:2009/07/21
Institute:Humboldt-Universität zu Berlin
Preprint Number:635
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