## Minimax pricing and Choquet pricing.(English)Zbl 1168.60355

Summary: The Choquet pricing and minimax pricing, which are nonlinear expectations, have been widely used in economics, finance and insurance as an alternative to traditional mathematical expectation. However, it is usually not easy to calculate these due to their nonlinearity. In this paper, we consider the calculation of a class of Choquet expectations and minimax expectations obtained from the pricing of a contingent claim with multiple prior probability measures. We show that both the Choquet pricing and minimax pricing of some European options are same, although this result is not in general true for non-European options.

### MSC:

 60H30 Applications of stochastic analysis (to PDEs, etc.) 28A12 Contents, measures, outer measures, capacities 91B30 Risk theory, insurance (MSC2010) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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### References:

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