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The relations of Choquet Integral and G-Expectation

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  • Ju Hong Kim

Abstract

In incomplete financial markets, there exists a set of equivalent martingale measures (or risk-neutral probabilities) in an arbitrage-free pricing of the contingent claims. Minimax expectation is closely related to the $g$-expectation which is the solution of a certain stochastic differential equation. We show that Choquet expectation and minimax expectation are equal in pricing European type options, whose payoff is a monotone function of the terminal stock price $S_T$.

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  • Ju Hong Kim, 2021. "The relations of Choquet Integral and G-Expectation," Papers 2102.10213, arXiv.org.
    • Handle: RePEc:arx:papers:2102.10213
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    References listed on IDEAS

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    1. Chen, Zengjing & Kulperger, Reg, 2006. "Minimax pricing and Choquet pricing," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 518-528, June.
    2. He, Kun & Hu, Mingshang & Chen, Zengjing, 2009. "The relationship between risk measures and choquet expectations in the framework of g-expectations," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 508-512, February.
    3. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    4. Hongxia Wang, 2015. "Conditional Choquet Expectation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(18), pages 3782-3795, September.
    5. Jiang, Long, 2009. "A necessary and sufficient condition for probability measures dominated by g-expectation," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 196-201, January.
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