Portfolio Selection In Behavioral Finance

we will generalize the behavioral portfolio selection problem and solve the behav-ioral portfolio selection problem with loss constraint, the Choquet minimization prob-lem with general risk measure and the behavioral portfolio selection problem withoutInada condition. The main context of the paper is listed below.The first chapter introduces the history and the current state of the portfolio selec-tion problem, then gives a brief review on some of the most important results.The second chapter studies the behavioral portfolio selection with loss constraint.This chapter adds some loss management to the model in Jin and Zhou [25], givesa priori bound to the loss and searches the optimal portfolio in this scenario. Thesolving schema is: first split the problem into positive part and negative part, then solveanother optimization problem, which connects the two parts. The additional technicalchallenge is that we have to solve a concave Choquet minimization problem with anadditional upper bound. The optimal terminal wealth profile is in general characterizedby three pieces: the agent has gains in the good states of the world, gets a moderate,endogenously constant loss in the intermediate states, and suffers the maximal loss(which is the given bound for losses) in the bad states. The contributions of the chapterareEconomically, the final solution exhibits quite different trading behaviors com-pared with their unconstrained counterparts: while the agent is still gambling (onthe good states of the world), she is more cautious in taking leverage so as tomeet the regulation on losses.Mathematically we completely solve an associated, unconventional Choquetminimization problem with both upper and lower constraints, in an infinite di-mensional space (the space of quantile functions).The third chapter studies the Choquet minimization problem with general riskmeasure. The format of the class of risk measure in this chapter is a linear function ofthe quantile function of the loss r.v.. Some special examples of the risk measure in thischapter are the maximum loss in the Chapter 2, the VaR and CVaR, which are popularin the bank industry. The main difficulty of behavioral portfolio selection problem with the risk measure is to solve a concave Choquet minimization problem with general riskmeasure. This chapter first study the relationship between the budget constraint andthe risk constraint, then prove that the optimal solution must be a step function withone/two steps. In the final we use CVaR as a special example to get a concrete solution.The fourth chapter studies the behavioral portfolio selection problem without In-ada condition, which include the cases with/without loss control. Inada condition as-sumes that the first order derivative of the positive part utility function is +∞. The mainresult of this chapter is: if there is no Inada condition, there is some positive probabilityon that the terminal wealth is identical with the reference point, i.e. it is a"zero gainand zero loss"state.The final chapter concludes.