Abstrakt
Classical Merton model assumest hat an asset is modelled by Brownian motion or geometric Brownian motion. However, these models lack some empirical properties of usual financial series.
If jumps are allowed into the model, it becomes much more appropriate. In this note, jump processes are briefly introduced.
Subsequently, the impact of jumps on the optimal consumption and portfolio choice is studied. Theoretical formulas of optimal values are presented and finally, a numerical study on real data is performed with rather notable results.