Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time

44 Pages Posted: 1 Jul 2020

See all articles by Ying Hu

Ying Hu

Université de Rennes 1

Hanqing Jin

Mathematical Institute; Oxford-Nie Financial Big Data Laboratory; St. Peter's College

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: June 3, 2020

Abstract

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 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 1 corresponding to an effective reduction in risk premium due to probability weighting.

Keywords: Rank-dependent utility, probability weighting, portfolio selection, continuous time, time inconsistency, intra-personal equilibrium strategy, market price of risk

Suggested Citation

Hu, Ying and Jin, Hanqing and Zhou, Xunyu, Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time (June 3, 2020). Available at SSRN: https://ssrn.com/abstract=3617346 or http://dx.doi.org/10.2139/ssrn.3617346

Ying Hu

Université de Rennes 1 ( email )

11 Rue Jean Macé
Rennes, Rennes 35042
France

Hanqing Jin (Contact Author)

Mathematical Institute ( email )

Andrew Wiles Building
Radicliff Observatory Quarter, Woodstock Road
Oxford, oxfordshire OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk

Oxford-Nie Financial Big Data Laboratory ( email )

Andrew Wiles Building
Woodstock Road
Oxford, Oxfordshire OX2 6GG
United Kingdom

St. Peter's College ( email )

New Inn Hall Street
Oxford, Oxfordshire OX1 2DL
United Kingdom

HOME PAGE: http://www.spc.ox.ac.uk

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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