Is a risk-neutral probability a special case of an invariant measure?

  • $\begingroup$ @ Jeff : Invariant with respect to what ? Unless you elaborate with much more details and/or references and definitions. I'll donwvote the thread. $\endgroup$
    – TheBridge
    Jul 12 '12 at 15:21
  • $\begingroup$ Pretty common knowledge that a probability is a measure map on the interval [0,1]. An invariant measure is invariant under f if the inverse mu(f-1(A)) = mu(A). My question revolves around whether a risk-neutral probability map is required to satisfy this condition in addition to mu(f(0))=mu(0) and mu(f(1))=mu(1). $\endgroup$
    – Jeff
    Jul 14 '12 at 22:35

No, you obtain a risk-neutral measure by any change of measure; invariance is far more restrictive. Because in your formula $\mu\circ f^{-1} (A)=\mu(A)$, it has to be for any $A$.

Risk-neutrality can be seen as a way to inject into your model a list of market prices you really want to not be exposed to: once they are taken into account (i.e. once you made your change of measure), the remaning is martingale.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.