No‐Arbitrage Pricing for Dividend‐Paying Securities in Discrete‐Time Markets with Transaction Costs

29 Pages Posted: 14 Sep 2015

See all articles by Tomasz R. Bielecki

Tomasz R. Bielecki

Illinois Institute of Technology

Igor Cialenco

Illinois Institute of Technology

Rodrigo Rodriguez

Illinois Institute of Technology

Date Written: October 2015

Abstract

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete‐time markets with dividend‐paying securities. Specifically, we show that the no‐arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk‐neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a contingent claim contract. Our results are illustrated with a vanilla credit default swap contract.

Keywords: arbitrage, fundamental theorem of asset pricing, transaction costs, consistent pricing system, liquidity, dividends, credit default swaps, interest rate swaps

Suggested Citation

Bielecki, Tomasz R. and Cialenco, Igor and Rodriguez, Rodrigo, No‐Arbitrage Pricing for Dividend‐Paying Securities in Discrete‐Time Markets with Transaction Costs (October 2015). Mathematical Finance, Vol. 25, Issue 4, pp. 673-701, 2015, Available at SSRN: https://ssrn.com/abstract=2659382 or http://dx.doi.org/10.1111/mafi.12038

Tomasz R. Bielecki (Contact Author)

Illinois Institute of Technology ( email )

Department of Applied Mathematics
10 W. 32nd Street
Chicago, IL 60616
United States
312 567 3185 (Phone)
312 567 3135 (Fax)

Igor Cialenco

Illinois Institute of Technology ( email )

Department of Applied Mathematics
10 West 32nd Str, Bld E1, Room 208
Chicago, IL 60616
United States
3125673131 (Phone)

HOME PAGE: http://math.iit.edu/~igor/

Rodrigo Rodriguez

Illinois Institute of Technology

Stuart Graduate School of Business
565 W. Adams St.
Chicago, IL 60661
United States

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