We study  dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ( 2005 ). We consider a financial market consists of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the drift uncertainty and volatility uncertainty of the stock price process.  A time consistent G-expectation is defined by the viscosity solution of the G-heat equation. Using the time consistent G-expectation we define the G dynamic pricing mechanism for the claim. We prove that G dynamic pricing mechanism is the bid-ask Markovian dynamic pricing mechanism. The full nonlinear PDE is derived to describe the bid (resp. ask) price dynamic of the claims. Monotone characteristic finite difference schemes for the nonlinear PDE are given,  and the simulations of the bid (resp. ask) prices of contingent claims with uncertainty are implemented.
We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ( 24 ). We consider a financial market consisting of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the drift uncertainty and volatility uncertainty of the stock price process. Using the techniques on G-framework we show that the risk premium of the asset is uncertain and distributed with maximum distribution. A time consistent G-expectation is defined by the viscosity solution of the G-heat equation. Using the time consistent G-expectation we define the G dynamic pricing mechanism for the claim. We prove that G dynamic pricing mechanism is the bid-ask Markovian dynamic pricing mechanism. The full nonlinear PDE is derived to describe the bid (resp. ask) price process of the claim. Monotone implicit characteristic finite difference schemes for the nonlinear PDE are given, nonlinear iterative schemes are constructed, and the simulations of the bid (resp. ask) prices of contingent claims under uncertainty are implemented.
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time consistent
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2005
24
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consists
consisting
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Using the techniques on G-framework we show that the risk premium of the asset is uncertain and distributed with maximum distribution.
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dynamic of the claims. Monotone
process of the claim. Monotone implicit
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nonlinear iterative schemes are constructed,
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with
under