Abstract
In this paper, we consider the problem of option pricing from the perspect of minimax algorithm, an online learning framework. We introduce numéraire, which is a unit of account in economics, to the market dynamic as a multi-round game between two players: the investor and the nature. In this way, we are able to apply the online learning framework namely minimax algorithm in game theory. We model the repeated games between the investor and the nature as a price process under different numéraires, thus permit arbitrary choice of numéraire, and study this model under no arbitrage condition of a complete market. We also relax the constraint of convex payoff functions in previous works by characterizing the explicit mixed-strategy Nash equilibrium in a single-round game, and then generalize this result to multi-round games.
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Hu, G., Xu, W. (2019). Robust Option Pricing Under Change of Numéraire. In: Xu, W., Xiao, L., Li, J., Zhu, Z. (eds) Computer Engineering and Technology. NCCET 2018. Communications in Computer and Information Science, vol 994. Springer, Singapore. https://doi.org/10.1007/978-981-13-5919-4_7
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DOI: https://doi.org/10.1007/978-981-13-5919-4_7
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