Behavioral portfolio selection with loss control |
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Authors: | Song Zhang Han Qing Jin Xun Yu Zhou |
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Institution: | [1]Department of Financial Mathematics, Peking University, Beijing 100871, P. R. China [2]Mathematical Institute and Nomura Centre for Mathematical Finance, The University of Oxford, 24-29 St Giles, Oxford OX1 3LB, UK [3]Oxford-Man Institute of Quantitative Finance, The University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6ED, UK [4]Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong |
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Abstract: | In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically
the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic
for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal
terminal wealth profile is in general characterized by 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. Examples are given to illustrate the general results. |
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Keywords: | Cumulative prospect theory portfolio choice gains and losses constraint Choquet integral quantile function |
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