## When optimization becomes irrelevant: time-inconsistency and its consequences

- Date: 01/31/2008

Lecturer(s):

Ivar Ekeland (University of British Columbia)

Location:

University of Victoria

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.

Other Information:

Special PIMS Lectures at UVIC 2008