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Risk minimization for game options in markets imposing minimal transaction costs

Part of: Limit theorems Mathematical finance Stochastic processes

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: [email protected]
** Postal address: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 9190401, Israel. Email address: [email protected]
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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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References

[1] Altarovici, A.,Muhle-Karbe, J. and Soner, H. M. (2015).Asymptotics for fixed transaction costs.Finance Stoch. 19,363–414.Google Scholar
[2] Cvitanić, J. and Karatzas, I. (1996).Backward stochastic differential equations with reflection and Dynkin games.Ann. Prob. 24,2024–2056.Google Scholar
[3] Dolinsky, Y. (2013).Hedging of game options with the presence of transaction costs.Ann. Appl. Prob. 23,2212–2237.Google Scholar
[4] Dolinsky, Y. (2014).Limit theorems for partial hedging under transaction costs.Math. Finance 24,567–597.Google Scholar
[5] Dolinsky, Y. and Kifer, Y. (2007).Hedging with risk for game options in discrete time.Stochastics 79,169–195.CrossRefGoogle Scholar
[6] Dolinsky, Y. and Kifer, Y. (2008).Binomial approximations of shortfall risk for game options.Ann. Appl. Prob. 18,1737–1770.Google Scholar
[7] Guasoni, P. (2002).Optimal investment with transaction costs and without semimartingales.Ann. Appl. Prob. 12,1227–1246.Google Scholar
[8] Guasoni, P. (2002).Risk minimization under transaction costs.Finance Stoch. 6,91–113.Google Scholar
[9] Iron, Y. and Kifer, Y. (2011).Hedging of swing game options in continuous time.Stochastics 83,365–404.Google Scholar
[10] Kamizono, K. (2003).Partial hedging under transaction costs.SIAM J. Control Optimization 42,1545–1558.Google Scholar
[11] Kifer, Y. (2000).Game options.Finance Stoch. 4,443–463.CrossRefGoogle Scholar
[12] Kifer, Y. (2006).Error estimates for binomial approximations of game options.Ann. Appl. Prob. 16,984–1033,2273–2275. (Correction: 18 (2008),1271–1277.)Google Scholar
[13] Kobylanski, M. and Quenez, M.-C. (2012).Optimal stopping time problem in a general framework.Electron. J. Prob. 17, 28pp.Google Scholar
[14] Korn, R. (1998).Portfolio optimisation with strictly positive transaction costs and impulse control.Finance Stoch. 2,85–114.CrossRefGoogle Scholar
[15] Lepeltier, J.-P. and Maingueneau, M. A. (1984).Le jeu de Dynkin en théorie générale sans l'hypothèse de Mokobodski.Stochastics 13,25–44.Google Scholar
[16] Lo, A. W.,Mamaysky, H. and Wang, J. (2004).Asset prices and trading volume under fixed transaction costs.J. Political Econom. 112,1054–1090.Google Scholar
[17] Morton, A. J. and Pliska, S. R. (1995).Optimal portfolio management with fixed transaction costs.Math. Finance 5,337–356.CrossRefGoogle Scholar
[18] Øksendal, B. and Sulem, A. (2002).Optimal consumption and portfolio with both fixed and proportional transaction costs.SIAM J. Control Optimization 40,1765–1790.Google Scholar