Talk:Numéraire

Change of Numeraire Technique
There should be a remark, that r(t) is a function, which denotes the interest rate at time t.

If this function is a constant rho, the expression simplifies to


 * M(t)=1*exp(rho*t)

Undefined terms
The article would (as always) be clearer if every term appearing in formulae or equations had a clear definition or description.

I take it that the purpose of showing these equations (and their derivations) is to acquaint non-mathematicians with compact formula of actual use in their pursuit of business or of economic theory. If so, we would of course not insist on mathematical rigour in such a context. However, the explanatory power of the exposition is considerably weakened if readers are left wondering - as I was - "What is F(x)?"

There is nothing in the article that makes it clear what the role or nature of F(x) is. Someone slightly familiar with statistics might assume, from the names of some linked articles, and from its appearing to the right of a vertical bar or pipe symbol "|", that it refers to a given probability distibution. Anyway, I did. Still, without chasing down all the links to other articles, I won't know if I was right to do so.

yoyo (talk) 05:54, 22 September 2009 (UTC)


 * By F(x) do you mean \mathcal{F}(t)? In that case, it is just a σ-field. 2604:3D09:797D:3500:29EE:46AA:900B:D836 (talk) 06:19, 31 December 2021 (UTC)

Abstract Bayes
The abstract Bayes formula is a formula in stochastic processes that is very different from Bayes rule, so the link to Bayes rule is not helpful. As described in Karatzas and Shreve (Lemma 3.5.3), the formula is: E[Z(T)Y|F_s] = (1/Z(s))E[YZ(t)|F_s] for 0 \leq s \leq t \leq T, and a martingale {Z(r),F_r} for r in [0,T]. Perhaps a new article on the abstract Bayes formula would be helpful.Vinzklorthos (talk) 21:49, 2 March 2012 (UTC)

naming
How is this usually spelled in English? — Preceding unsigned comment added by 76.120.175.135 (talk) 22:02, 21 January 2014 (UTC)