# A Sigh is Just A Sigh

I was talking to a graduate student the other day, and he referred me to the “fundamental theorem of finance”.Isn’t it strange? I thought later, that finance should have a fundamental theorem (and that I wasn’t quite sure what it was). Axiomatic systems have theorems. If you google “the fundamental theory of chemistry” you won’t find much because chemistry isn’t about axioms. Here is what you find if you google “fundamental theorem of arithmetic/algebra/calculus/finance”.

° The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a unique product of prime numbers

° The fundamental theorem of algebra states that every polynomial equation of degree n with complex number coefficients has n complex roots.

° The first fundamental theorem of calculus states that, if f is continuous on the closed interval [a,b] and F is the antiderivative (indefinite integral) of f on [a,b], then the definite integral of f(x) from a to b is F(b) – F(a).

So far I get it.

Now … … (wait for it):

° Fundamental Theorem of Finance. Security prices exclude arbitrage if and only if there exists a strictly positive value functional, under the technical restrictions that the space of portfolios and the space of contingent claims are locally convex topological vector spaces and the positive cone of the space of contingent claims is compactly generated, that is, there exists a compact set K of X (not containing the null element of X ) such that C = {x ? X : x ? 0} = U ?K for ?>= 0

You must remember this / A kiss is still a kiss / A sigh is just a sigh / The fundamental things apply / As time goes by.

Originally published at Wilmott.com and reproduced here with the author’s permission.

### 2 Responses to "A Sigh is Just A Sigh"

1. Richard4691   February 19, 2009 at 10:28 am

I would like to point out to you that the majority of the names on your list of institutions that have put the system at risk are not and were not banks that would fall under the Basel accord. Now in the response to the crisis, many formerly non-bank financial insitutions have sought bank charters in order to gain access the Fed and the Fed,at the same time, has become the savior of just about everything. Before you can regulate a bank, you need to have a precise definition of bank. I am going to propose that one part of the definition might be that a bank is an entity that properly accounts for its positions at cost and which periodically evaluates the adequacy of its valuation reserves, taking a charge to income or recognizing it as the level of reverses is adjusted. Financial institutions that rightly accounts for its positions using a mark-to-market metric are something else and it appears to be these that pose systemic risk.

• Anonymous   March 12, 2009 at 2:10 pm

I would like to point out to you that the majority of the names on your list of institutions that have put the system at risk are not and were not banks that would fall under the Basel accord. Now in the response to the crisis, many formerly non-bank financial insitutions have sought bank charters in order to gain access the Fed and the Fed,at the same time, has become the savior of just about everything. Before you can regulate a bank, you need to have a precise definition of bank. I am going to propose that one part of the definition might be that a bank is an entity that properly accounts for its positions at cost and which periodically evaluates the adequacy of its valuation reserves, taking a charge to income or recognizing it as the level of reverses is adjusted. Financial institutions that rightly accounts for its positions using a mark-to-market metric are something else and it appears to be these that pose systemic risk.