Advances in Applied Probability

Risk minimization for game options in markets imposing minimal transaction costs

Yan Dolinsky and Yuri Kifer

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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.

Article information

Adv. in Appl. Probab., Volume 48, Number 3 (2016), 926-946.

First available in Project Euclid: 19 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91G10: Portfolio theory 91G20: Derivative securities
Secondary: 60F15: Strong theorems 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G44: Martingales with continuous parameter

Game option transaction cost hedging with friction risk minimization


Dolinsky, Yan; Kifer, Yuri. Risk minimization for game options in markets imposing minimal transaction costs. Adv. in Appl. Probab. 48 (2016), no. 3, 926--946.

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