The Cox-Ingersoll-Ross process under volatility uncertainty. (English) Zbl 1539.60062
Summary: Due to the significance of the Cox-Ingersoll-Ross process in various areas of finance, a wide range of studies and investigations on this model have been carried out. In cases of ambiguity, we characterize it by applying the theory of \(G\)-expectation and the associated \(G\)-Brownian motion. In this paper, we establish the existence and uniqueness of the solution for the Cox-Ingersoll-Ross process in the presence of volatility uncertainty. In addition, certain properties of the solution are indicated, such as regularity and the strong Markov property. Furthermore, we compute some moments of the Cox-Ingersoll-Ross process by employing an extension of the nonlinear Feynman-Kac theorem.
MSC:
| 60G65 | Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
Keywords:
Cox-Ingersoll-Ross process; volatility uncertainty; existence and uniqueness; strong Markov property; nonlinear Feynman-Kac theoremReferences:
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