DYNAMIC CONIC FINANCE: PRICING AND HEDGING IN MARKET MODELS WITH TRANSACTION COSTS VIA DYNAMIC COHERENT ACCEPTABILITY INDICES

Tomasz R. Bielecki (), Igor Cialenco (), Ismail Iyigunler () and Rodrigo Rodriguez ()
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Tomasz R. Bielecki: Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA
Igor Cialenco: Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA
Ismail Iyigunler: Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA
Rodrigo Rodriguez: Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 01, 1-36

Abstract: In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.

Keywords: Dynamic coherent acceptability index; conic finance; dynamic coherent risk measures; transaction costs; dividend paying securities; swap contracts; no-good-deal bounds; fundamental theorems of asset pricing; dynamic bid and ask; dynamic gain-loss ratio; arbitrage pricing; illiquid market (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (8)

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DOI: 10.1142/S0219024913500027

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