Risk minimization for game options in markets imposing minimal transaction costs. (English) Zbl 1380.91129

Dolinsky, Yan; Kifer, Yuri

Adv. Appl. Probab. 48, No. 3, 926-946 (2016).

Summary: 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.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
91G10	Portfolio theory
60G40	Stopping times; optimal stopping problems; gambling theory
60G44	Martingales with continuous parameter
60F15	Strong limit theorems
91G60	Numerical methods (including Monte Carlo methods)

Keywords:

game option; transaction cost; hedging with friction; risk minimization