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Consistent investment of sophisticated rank‐dependent utility agents in continuous time
Author(s) -
Hu Ying,
Jin Hanqing,
Zhou Xun Yu
Publication year - 2021
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12315
Subject(s) - isoelastic utility , portfolio , weighting , expected utility hypothesis , mathematical economics , economics , mathematical optimization , function (biology) , rank (graph theory) , subgame perfect equilibrium , scaling , mathematics , econometrics , finance , geometry , nash equilibrium , combinatorics , evolutionary biology , biology , medicine , radiology
We study portfolio selection in a complete continuous‐time market where the preference is dictated by the rank‐dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of a sophisticated consistent planners who seek (subgame perfect) intra‐personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than one corresponding to an effective reduction in risk premium due to probability weighting.