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Dynamic utility-based good deal bounds

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  • Klöppel Susanne
  • Schweizer Martin

Abstract

We introduce and study no-good-deal valuation bounds defined in terms of expected utility. A utility-based good deal is a payoff whose expected utility is too high in comparison to the utility of its price. Forbidding good deals induces, via duality, restrictions on pricing kernels and thereby gives tighter valuation bounds on payoffs than absence of arbitrage alone. Our approach extends earlier work by Černý (2003) in several directions: We give rigorous results for a general probability space instead of finite Ω; we systematically use duality results to provide a streamlined approach with simple arguments; we do all this rigorously for both static and dynamic situations; and we give a systematic comparison between local and global (conditional) pricing kernel restrictions for the temporally dynamic setting. For the dynamic case, we show in a Lévy framework that defining no-good-deal valuation measures by imposing local conditional restrictions on their instantaneous market prices of risk gives valuation bounds having very good dynamic properties as processes over time. We also show that global restrictions cannot yield such results in general.

Suggested Citation

  • Klöppel Susanne & Schweizer Martin, 2007. "Dynamic utility-based good deal bounds," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 1-25, October.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:4/2007:p:25:n:3
    DOI: 10.1524/stnd.2007.0905
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    References listed on IDEAS

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    1. Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
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    5. Longarela, Iñaki R., 2001. "An Extension of Good-Deal Asset Price Bounds," SSE/EFI Working Paper Series in Economics and Finance 0448, Stockholm School of Economics, revised 19 Oct 2001.
    6. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161, April.
    7. Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627, October.
    8. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
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    Cited by:

    1. Jocelyne Bion-Nadal & Giulia Nunno, 2013. "Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞," Finance and Stochastics, Springer, vol. 17(3), pages 587-613, July.
    2. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    3. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
    4. Laurence Carassus & Emmanuel Temam, 2010. "Pricing and Hedging Basis Risk under No Good Deal Assumption," Working Papers hal-00498479, HAL.

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