Chapter 8. A Continuous Minimax Strategy For Options Hedging

2009 ◽  
pp. 179-246
Keyword(s):  
Minimax Strategy ◽  
Options Hedging ◽  
Continuous Minimax

scholarly journals Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables

2018 ◽  
Vol 20 (01) ◽  
pp. 1750030 ◽  
Author(s):  
Atsuhiro Satoh ◽  
Yasuhito Tanaka
Keyword(s):  
Nash Equilibrium ◽  
Objective Function ◽  
The Other ◽  
Minimax Strategy ◽  
Equilibrium Strategies ◽  
Minimax Strategies ◽  
Nash Equilibrium Strategies ◽  
Special Case ◽  
Maximin Strategy

We examine maximin and minimax strategies for players in a two-players game with two strategic variables, [Formula: see text] and [Formula: see text]. We consider two patterns of game; one is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s, and the other is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s. We call two players Players A and B, and will show that the maximin strategy and the minimax strategy in the [Formula: see text]-game, and the maximin strategy and the minimax strategy in the [Formula: see text]-game are all equivalent for each player. However, the maximin strategy for Player A and that for Player B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the [Formula: see text]-game nor the [Formula: see text]-game. But, in a special case, where the objective function of Player B is the opposite of the objective function of Player A, the maximin strategy for Player A and that for Player B are equivalent, and they constitute the Nash equilibrium both in the [Formula: see text]-game and the [Formula: see text]-game.

Recurrent Objections to the Minimax Strategy

1959 ◽  
Vol 41 (1) ◽  
pp. 36 ◽  
Author(s):  
Anthony Y. C. Koo
Keyword(s):  
Minimax Strategy

Currency options: Hedging and social value

1987 ◽  
Vol 31 (1-2) ◽  
pp. 246-256 ◽  
Author(s):  
Dieter Sondermann
Keyword(s):  
Social Value ◽  
Currency Options ◽  
Options Hedging

scholarly journals Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 671 ◽  
Author(s):  
Jihwan Kim ◽  
Donghoon Ha ◽  
Younghun Kwon
Keyword(s):  
Optimal Strategy ◽  
Quantum States ◽  
Minimax Strategy ◽  
Minimum Error ◽  
Optimal Measurement ◽  
Single Side ◽  
Quantum Ensemble ◽  
Zero Sum ◽  
Necessary And Sufficient ◽  
Specific Quantum

This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the receiver may obtain the minimum information about quantum states, but the receiver performs an optimal measurement to obtain guessing probability for the quantum ensemble prepared by the sender. Therefore, knowing whether the optimal strategy of the game is unique is essential. This is because there is no alternative if the optimal strategy is unique. This paper proposes the necessary and sufficient condition for an optimal strategy of the sender to be unique. Also, we investigate the quantum states that exhibit the minimum guessing probability when a sender’s minimax strategy is unique. Furthermore, we show that a sender’s minimax strategy and a receiver’s minimum error strategy cannot be unique if one can simultaneously diagonalize two quantum states, with the optimal measurement of the minimax strategy. This implies that a sender can confirm that the optimal strategy of only a single side (a sender or a receiver but not both of them) is unique by preparing specific quantum states.

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