2022/05/31 by David Criens, Criens, David, Lars Niemann +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Control Systems Optimization #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2205.15692
openalex publication_date 2022/05/31 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
In this note we consider a family of nonlinear (conditional) expectations that can be understood as a multidimensional diffusion with uncertain drift and certain volatility. Here, the drift is prescribed by a set-valued function that depends on time and path in a Markovian way. We establish the Feller property for the associated sublinear Markovian semigroup and we observe a smoothing effect as our framework carries enough randomness. Furthermore, we link the corresponding value function to a semilinear Kolmogorov equation.