English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we investigate possible approaches to study generaltime-inconsistent optimization problems without assuming the existence ofoptimal strategy. This leads immediately to the need to refine the concept oftime-consistency as well as any method that is based on Pontryagin's MaximumPrinciple. The fundamental obstacle is the dilemma of having to invoke the {\itDynamic Programming Principle} (DPP) in a time-inconsistent setting, which iscontradictory in nature. The main contribution of this work is the introductionof the idea of the "dynamic utility" under which the original time inconsistentproblem (under the fixed utility) becomes a time consistent one. As a benchmarkmodel, we shall consider a stochastic controlled problem with multidimensionalbackward SDE dynamics, which covers many existing time-inconsistent problems inthe literature as special cases, and we argue that the time inconsistency isessentially equivalent to the lack of {\it comparison principle}. We shallpropose three approaches aiming at reviving the DPP in this setting: theduality approach, the dynamic utility approach, and the master equationapproach. Unlike the game approach in many existing works in continuous timemodels, all our approaches produce the same value as the original staticproblem.

Dynamic Approaches for Some Time Inconsistent Problems