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Risk minimization for game options in markets imposing minimal transaction costs

Part of: Mathematical finance Stochastic processes Limit theorems

Published online by Cambridge University Press:  19 September 2016

Yan Dolinsky  and
Yuri Kifer
Yan Dolinsky*
Affiliation:
The Hebrew University of Jerusalem
Yuri Kifer*
Affiliation:
The Hebrew University of Jerusalem
*
* Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel. Email address: yan.dolinsky@mail.huji.ac.il
** Postal address: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 9190401, Israel. Email address: kifer@ma.huji.ac.il
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Abstract

We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction cost. We prove that in the continuous-time Black‒Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model.

Keywords

Game optiontransaction costhedging with frictionrisk minimization

MSC classification

Primary: 91G10: Portfolio theory 91G20: Derivative securities
Secondary: 60F15: Strong theorems 60G40: Stopping times; optimal stopping problems; gambling theory 60G44: Martingales with continuous parameter
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 3 , September 2016 , pp. 926 - 946
Copyright
Copyright © Applied Probability Trust 2016 

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