Document Type


Degree Name

Master of Science (MSc)




Faculty of Science

First Advisor

George Lai

Advisor Role

Thesis Supervisor

Second Advisor

Joe Campolieti

Advisor Role

Thesis Supervisor


In the case of minimizing risk with a given level of expected return, we discuss the portfolio selection problem with the asset returns are characterized by a Gaussian distribution and heavy tailed distribution.

More specifically, under the Gaussian assupmtion, we give the explicit solutions to the problems of minimizing risk variance, CaR and EaR respectively. When a compound Poisson process is assumed, we derive explicit solutions to the variance, CaR and EaR. Furthermore, we give the explicit soultion for the CaR when a Lévy distribution is considered.

For the more realistic process-normal inverse process, we are able to obtain the analytical solution for the EaR with the help of the explicit form of its probability density function.

Moreover, we give numerical results using Monte Carlo simulation for each risk measure discussed above by assuming that the stock return follow Gaussian and Compound Poisson models, respectively. Finally, we give a comparison of the risk curves between these two processes and characterize the sensitivity of the risk curves for various values of the model parameters.

Convocation Year


Included in

Mathematics Commons