In the setting of Exercise 8.1, let P denote the physical probability and assume E Pt+1
Question:
In the setting of Exercise 8.1, let P denote the physical probability and assume E
Pt+1 +Dt+1 Pt
= Rf .
Suppose there is an infinite horizon. Show that there is no probability Q on the space of infinite paths that is
(a) equivalent to P, and
(b) satisfies E∗
t
Pt+1 + Dt+1 Pt
= Rf for each t, whereE∗ denotes expectation with respecttoQ. Hint: Applythe strong law of large numbers to show that any Q satisfying
(b) cannot be equivalent to P.
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