Topics

• Task 1: Simulating dynamic utilities and related non-linear forward HJB-SPDEs

Task 1.a. Simulating dynamic utilities in the jumps case

Task 1b. Multi-level Monte Carlo methods (MLMC)

Task 1.c. Deep learning for simulating the related Stochastic HJB equation

• Task 2: Surveillance of multiple sources of risk

Task 2.a. Detection in a multivariate setting

Task 2.b. Hitting probabilities: multidimensional approximations

Task 2.c. Example of random utilities with switching environment

Task 2.d. Multivariate risk measures: numerical schemes, simulation and calibration

• Task 3: Estimation and Calibration of dynamic utilities in multivariate setting

Task 3.a. Deep-Learning approach for dynamic utilities

Task 3.b. Learning agent Utilities and robo advisors

Task 3.c. Estimation of dependence structures

Task 3.d. Approximate Bayesian Computation

• Task 4: Decision theory with moral hazard and Robust control

Task 4.a. Principal agent problem with dynamic utility criteria

Task 4.b. Numerical schemes for dynamic forward utilities under uncertainty