Behavioral portfolio optimization with social reference point

In this study, we address the social interaction process in which PT (Prospect Theory) preferences are influenced by other market participants, e.g., regular CRRA (Constant Relative Risk Averse) investors or other PT investors, and study then the long run wealth convergence of the two trading parties: one PT agent vs. one CRRA agent or both agents of PT types. In the model with one PT agent vs. one CRRA agent, the PT agent knows the CRRA agent’s optimal terminal wealth and takes it as his/her reference point. If the PT agent starts with an initial wealth level higher than that of the CRRA agent, he/she will always do better than the CRRA agent by imitating the CRRA agent’s policy. On the other hand, if the PT agent starts with a wealth level lower than that of the CRRA agent, he/she can still do better than the CRRA agent by adopting a “gambling policy”. When both trading parties are of PT type, we consider two types of reference points: either both PT agents take their average wealth as their reference point or they are mutually reference dependent. Under both situations, we give sufficient conditions on the long run wealth convergence.