Bernanke took questions from teachers at the Federal Reserve Board.
Note video is down and on the extreme right.
One question was how do they teach savings with interest rates so low.
Bernanke said interest rates were low for a reason, to stimulate the economy. He said investing won’t pan out if the economy goes down, and the low rates are needed according to Bernanke to prevent that from happening.
Financial math is about recursion. Accumulation at a rate of interest is recursion.
B(n’) = (1+r)*B(n)
B(0) = initial balance.
where B(n) is savings balance at period n. Here n’ is n+1. The value of r is the rate of interest.
The function B(n) exists by this definition by the Dedekind 1888 Recursion Theorem. It exists by appending the ordered pair (n’,(1+r)*B(n)) to the other ordered pairs of the function for values from 0 to n.
On personal interest, Bernanke praised the Double Decay Model of Beaglehole Tenney for use in what are called economic scenario generators in 2004.
A more recent interest rate generator with regime switching is discussed at this presentation at the 2011 Society of Actuaries Valuation Actuary Symposium.
The talks by Faye Albert and Mark Tenney are on this new model.
Again, the evolution of interest rates is recursive, but now we have branching as different paths are followed.
This means the r in the accumulation equation becomes r(n,p) where p indexed the path.
This helps answer the question of what is math good for?
What is recursion good for? Addition, multiplication, exponential growth, bank balance growth, stochastic simulation of interest rates, risk management of banks and insurance companies, capital required for borrowing and taking risk with the money by banks and insurance companies.
Note the SOA talk above shows that the Academy of Actuaries ESG does not work very well compared to the Mathematical Finance Company ESG. So one model can be better than another. This can make the difference of financial ruin of a bank or insurance company or survival in a crisis.
During Bernanke’s talk and the Q and A, the cost of college came up.
Should everyone go to college?
Bernanke said no. You only go to college if you can make enough money with the credential and skills you get to pay off your college debt.
What jobs pay that well? Jobs that use economic scenario generators would fall into that category. Learning recursion helps you learn probability and stochastic simulation of banks and insurance companies. That can get you a job as an actuary or risk management professional or bond or derivatives trader at a bank or hedge fund. That will let you pay off your college loan and buy a house. So that’s what math is good for.
That is what recursion is good for. That is what the Peano Axioms are good for. That is what probability and financial math are good for.
==Summer Sale 2.99.
The book has 178 Examples, 463 Exercises, 98 definitions, 45 Lemmas with proofs, references to over 96 webpages, 58 chapters, and is 391 pages when formatted as pdf with Latex. The book is however not a pdf and is 100 percent html with no pdf, jpeg or pngs.
This book will teach you recursion and mathematical induction.
Typical treatments of the Peano Axioms cover the same material as in the book in about 20 pages or less. They usaully have few examples and the few exercises are as difficult as the theory.
In contrast, this text has many examples too trivial for the current texts on the Peano Axioms to cover. Building at a very slow pace with many numerical examples, the reader is taken through the Peano Axioms themselves, simple consequences, order of natural numbers, and simple identities used to prove the properties of addition. This build up includes many very simple proofs by mathematical induction.
There are no quadratic or higher algebraic formulas in the book. Complicated algebra formulas are the main stumbling block to learning mathematical induction. None are in the book, yet there are many worked out proofs of simple relationship using mathematical induction and simple problems for students to do.
The e-books in this series are 100 percent html. No pdf and no jpegs or pngs. They are completely in html and will resize on any device used to read them. They are fully searchable. You can take notes on any field or equation.