2023/10/16 by David Criens, Criens, David, Lars Niemann +1
Economics, Econometrics and Finance · Social Sciences · #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2310.10546
openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a time and path-dependent set-valued function. We show that the associated control problem coincides with both its weak and relaxed counterparts. Furthermore, we establish regularity properties of the value function and discuss their relation to Feller properties of nonlinear semigroups. In the Markovian case we provide conditions that allow us to identify the corresponding semigroup as the unique viscosity solution to a nonlinear Hamilton-Jacobi-Bellman equation. To illustrate our results we discuss a random G-double exponential Lévy setting.