In this paper we formulate a continuous-time behavioral （4 la cumulative prospect theory） portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically the model is motivate...In this paper we formulate a continuous-time behavioral （4 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.展开更多
We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution.We present two special cases for nonlinear g where the g-expectation of dis...We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution.We present two special cases for nonlinear g where the g-expectation of distributions can be explicitly derived.As a related problem,we introduce the notion of law-invariant g-expectation and provide its sufficient conditions.Examples of application in financial dynamic portfolio choice are supplied.展开更多
文摘In this paper we formulate a continuous-time behavioral （4 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.
基金NSFC(Grant No.11971409)The Hong Kong RGC(GRF,Grant No.15202421)+3 种基金The PolyU-SDU Joint Research Center on Financial MathematicsThe CAS AMSS-POLYU Joint Laboratory of Applied MathematicsThe Hong Kong Polytechnic UniversityXun Yu Zhou acknowledges financial support through a start-up grant and the Nie Center for Intelligent Asset Management at Columbia University.
文摘We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution.We present two special cases for nonlinear g where the g-expectation of distributions can be explicitly derived.As a related problem,we introduce the notion of law-invariant g-expectation and provide its sufficient conditions.Examples of application in financial dynamic portfolio choice are supplied.
