Jean-Paul Murara: The Investment-Consumption Problem with Stochastic Behaviour

The Merton investment-consumption optimal control problem is modified considering a non-constant volatility. We specifically modify this problem using the Jourdain-Sbai model, and then the Greselak-Ooosterlee-Van Vereen model. Different utility functions are also used and we derive their corresponding Hamilton-Jacobi-Bellman equations. After obtaining the optimal controls, different investment strategies are constructed, and related simulations are performed.