We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine processes.This is done as follows:given a setof parameters for the process,we construct a correspondin...We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine processes.This is done as follows:given a setof parameters for the process,we construct a corresponding nonlinear expectation on the path space of continuous processes.By a general dynamic programming principle,we link this nonlinear expectation to a variational form of the Kolmogorov equation,where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in.This nonlinear affine process yields a tractable model for Knightian uncertainty,especially for modelling interest rates under ambiguity.We then develop an appropriate Ito formula,the respective term-structure equations,and study the nonlinear versions of the Vasiˇcek and the Cox–Ingersoll–Ross(CIR)model.Thereafter,we introduce the nonlinear Vasicek–CIR model.This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence this approach solves the modelling issue arising with negative interest rates.展开更多
文摘We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine processes.This is done as follows:given a setof parameters for the process,we construct a corresponding nonlinear expectation on the path space of continuous processes.By a general dynamic programming principle,we link this nonlinear expectation to a variational form of the Kolmogorov equation,where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in.This nonlinear affine process yields a tractable model for Knightian uncertainty,especially for modelling interest rates under ambiguity.We then develop an appropriate Ito formula,the respective term-structure equations,and study the nonlinear versions of the Vasiˇcek and the Cox–Ingersoll–Ross(CIR)model.Thereafter,we introduce the nonlinear Vasicek–CIR model.This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence this approach solves the modelling issue arising with negative interest rates.
