Effects of heavy tails on optimal investment and consumption

We study the effect of heavy tails on optimal proportion and consumption problem, i.e. we compare the optimal and Merton proportion and consumption and compute the wealth loss. We state and show that the effect of heavy tails is quite slight in usual conditions. The effect stays nonsignificant even if we contaminate the Levy measure of the risky asset dynamics by severe drops of price. However, we observe that heavy tails need to be taken into account if an investor is exposed to a very huge loss or even bancruptcy. This could be the case of a very aggressive investor. Finally, we study the lower bound of the optimal investment proportion. We show that even for infinite kurtosis the optimal investment proportion is still positive. We also studied the rate of convergence to zero of the optimal investment proportion as the volatility/risk averse coefficient approaches infinity or expected return approaches zero.