Uncertainty and Probability Optimal Stopping

Time Consistency

With generalP, one runs easily into inconsistencies in dynamic

settings (Sarin/Wakker)

Time consistency⇐⇒law of iterated expectations:

Qmin∈PEQ

[

ess infP∈P EP[X|Ft]

]

= minP∈PEPX

Literature on time consistency in decision theory /risk measure theory

Epstein/Schneider, R. , Artzner et al., Detlefsen/Scandolo, Peng,

Chen/Epstein

time consistency is equivalent tostability under pasting:

letP,Q∈Pand let (pt),(qt) be the density processes

fix a stopping timeτ

define a new measureRvia setting

rt=

{ p

t ift≤τ

pτqt/qτ else

thenR∈Pas well