Stochastic maximum principle under probability distortion
Qizhu Liang, Jie Xiong
TL;DR
This paper develops a stochastic maximum principle for portfolio optimization under probability distortion, incorporating behavioral utility functions and providing necessary optimality conditions in continuous time.
Contribution
It introduces a necessary optimality condition for portfolio selection problems with probability distortion and S-shaped utilities within a continuous-time framework.
Findings
Derived a necessary condition for optimality under probability distortion.
Applied the theoretical results to multiple portfolio optimization examples.
Extended stochastic control methods to behavioral finance models.
Abstract
Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortions, a necessary condition for optimality is derived. The results are applied to various examples.
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Taxonomy
TopicsStochastic processes and financial applications · Risk and Portfolio Optimization · Economic theories and models