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multistage risk premium; utility function; portfolio optimization; multistage stochastic programming
This paper deals with a multistage stochastic programming portfolio selection problem with a new type of risk premium constraints. These risk premiums are constructed on the multistage scenario tree. Two ways of the construction are introduced and compared. The risk premiums are incorporated in the multistage stochastic programming portfolio selection problem. The problem maximizes the multivariate (multiperiod) utility function under condition that the multistage risk premiums are smaller than a prescribed level. The problem does not assume any separability of the multiperiod utility function. The performance of the suggested models is demonstrated for several kinds of multiperiod utility functions and several formulations of the multistage risk premium constraints. In all cases, including the risk premium constraints avoids the riskier positions.
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