On shortfall risk minimization for game options
Volume 7, Issue 4 (2020), pp. 379–394
Pub. online: 29 October 2020
Type: Research Article
Open Access
Open Access
Received
13 July 2020
13 July 2020
Revised
21 September 2020
21 September 2020
Accepted
22 October 2020
22 October 2020
Published
29 October 2020
29 October 2020
Abstract
In this paper we study the existence of an optimal hedging strategy for the shortfall risk measure in the game options setup. We consider the continuous time Black–Scholes (BS) model. Our first result says that in the case where the game contingent claim (GCC) can be exercised only on a finite set of times, there exists an optimal strategy. Our second and main result is an example which demonstrates that for the case where the GCC can be stopped on the whole time interval, optimal portfolio strategies need not always exist.
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