Affine processes under parameter uncertainty  

作　　者：Tolulope Fadina Ariel Neufeld Thorsten Schmidt 

机构地区：[1]Department of Mathematical Stochastics,University of Freiburg,Ernst-Zermelo Str.1,79104 Freiburg,Germany [2]Nanyang Technological University,Division of Mathematical Sciences,Singapore,Singapore [3]Freiburg Institute of Advanced Studies(FRIAS),Freiburg im Breisgau,Germany [4]University of Strasbourg Institute for Advanced Study(USIAS),Strasbourg,France

出　　处：《Probability, Uncertainty and Quantitative Risk》2019年第1期80-114,共35页概率、不确定性与定量风险（英文）

摘　　要：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.

关 键 词：Affine processes Knightian uncertainty Riccati equation Vasicek model Cox-Ingersoll-Ross model Nonlinear Vasicek/CIR model Heston model Ito formula Kolmogorov equation Fully nonlinear PDE SEMIMARTINGALE 

分 类 号：O17[理学—数学]