When optimization becomes irrelevant: time-inconsistency and its consequences
Topic
In optimal control, one traditionally discounts the future at a constant
rate: a gain u occurring at time t>0 is valued today at u exp(-rt),
where r is the discount rate. If non-constant discount rates are used,
as they should be for many reasons, then time-inconsistency occurs:
policies that seem optimal at time t=0 no longer will seem optimal when
the time to apply them comes. This has many interesting mathematical
consequences, including an integral equation which generalizes the
classical Hamilton-Jacobi equation, and which, in a simple case, reduces
to an implicit differential equation.
rate: a gain u occurring at time t>0 is valued today at u exp(-rt),
where r is the discount rate. If non-constant discount rates are used,
as they should be for many reasons, then time-inconsistency occurs:
policies that seem optimal at time t=0 no longer will seem optimal when
the time to apply them comes. This has many interesting mathematical
consequences, including an integral equation which generalizes the
classical Hamilton-Jacobi equation, and which, in a simple case, reduces
to an implicit differential equation.
Speakers
Additional Information
Special PIMS Lectures at UVIC 2008
Ivar Ekeland (University of British Columbia)
Ivar Ekeland (University of British Columbia)