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Dynamic Mean-Variance Optimization Problems with Deterministic Information


Sikic, Mario; Schweizer, Martin; Zivoi, Danijel (2018). Dynamic Mean-Variance Optimization Problems with Deterministic Information. International Journal of Theoretical and Applied Finance, 21(02):1850011.

Abstract

We solve the problems of mean-variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process S is a semimartingale, but not adapted to the filtration G which models the information available for constructing trading strategies. We choose as G=Fdet the zero-information filtration and assume that S is a time-dependent affine transformation of a square-integrable martingale. This class of processes includes in particular arithmetic and exponential Lévy models with suitable integrability. We give explicit solutions to the MVH and MVPS problems in this setting, and we show for the Lévy case how they can be expressed in terms of the Lévy triplet. Explicit formulas are obtained for hedging European call options in the Bachelier and Black-Scholes models.

Abstract

We solve the problems of mean-variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process S is a semimartingale, but not adapted to the filtration G which models the information available for constructing trading strategies. We choose as G=Fdet the zero-information filtration and assume that S is a time-dependent affine transformation of a square-integrable martingale. This class of processes includes in particular arithmetic and exponential Lévy models with suitable integrability. We give explicit solutions to the MVH and MVPS problems in this setting, and we show for the Lévy case how they can be expressed in terms of the Lévy triplet. Explicit formulas are obtained for hedging European call options in the Bachelier and Black-Scholes models.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2 April 2018
Deposited On:18 Feb 2020 10:10
Last Modified:18 Feb 2020 13:11
Publisher:World Scientific Publishing
ISSN:1793-6322
OA Status:Closed
Publisher DOI:https://doi.org/10.1142/S0219024918500115
Official URL:https://www.worldscientific.com/doi/abs/10.1142/S0219024918500115
Other Identification Number:merlin-id:17802

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