Ever since von Neumann and Morgenstern published the axiomisation of
Expected Utility Theory, there have been a considerable amount of ob-
servations appeared in the literature violating the expected utility theory.
To make decisions under uncertainty, people generally separate possible
outcomes into gains and losses. They are risk averse for gains but risk
seeking for losses with very large probabilities; risk averse for losses but
risk seeking for gains with very small probabilities. To accommodate
these characteristics, Prospect Theory and its improvement Cumulative
Prospect Theory were developed in order to formulate people's behaviours
under uncertainty in a descriptive and normative way. As such, values are
assigned to gains and losses and probabilities are replaced by probability
weighting functions. The CPT models built in this project are based on
the power value function and the compound invariant form of probability
weighting function. The models are calibrated with the data from Hong
Kong Mark Six lottery market. The parameters in the models are esti-
mated, hence to examine properties of the models and give an insights into
how they fit the real life situation. In the first approach, the parameter
in the value function is fixed, but the plots of the estimated probability
weighting function do not give sensible explanations of lottery player's
behaviours. In the second approach, the parameters in value function and
weighting function are both estimated from the data to give an optimal
fitting of the model
