While at AIMS, Paul studied a utility maximization or optimal investment problem in the presence of a stochastic endowment that cannot be traded in financial market. He used the dynamic programming approach to solve the optimization problem and derived the Hamiltonian-Jacobi-Bellman (HJB) equation for the value function for the control problem which is a non linear PDE. Furthermore, he developed a finite difference method with implicit timestepping and non-equidistant grid to solve the resulting non-linear reduced HJB equation and also derived the optimal investment strategy and discuss its asymptotic behaviour.

Paul currently works as Academic assistant at BTU cottbus-senftenberg in Germany where he has already submitted his thesis and is currently preparing the defense.