Heterogeneous Homebuyers, Mortgage Choice and the use of Mortgage Brokers

Choosing a mortgage product in the face of labor income risk, interest rate risk and borrowing constraints is one of the most important decisions facing a household. This paper investigates the choice between a variety of fixed rate mortgages and adjustable rate mortgages. We find that households with a high loan-to-value ratio, risky income and high risk aversion are more likely to choose a fixed rate mortgage. Choosing a mortgage product relies market search and information. The paper finds that in general first-time homebuyers and those with a high loan-to-value ratio are more likely to use a mortgage broker.Mortgage choice,First-time homebuyer,Mortgage broker

Integrating factors for second order ODEs

A systematic algorithm for building integrating factors of the form mu(x,y), mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without solving any differential equations, except for a linear ODE in one subcase of the mu(x,y) problem. Examples of ODEs not having point symmetries are shown to be solvable using this algorithm. The scheme was implemented in Maple, in the framework of the "ODEtools" package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling non-linear examples from Kamke's book is shown.Comment: 21 pages - original version submitted Nov/1997. Related Maple programs for finding integrating factors together with the ODEtools package (versions for MapleV R4 and MapleV R5) are available at http://lie.uwaterloo.ca/odetools.ht

Variations on the Sum-Product Problem

This paper considers various formulations of the sum-product problem. It is shown that, for a finite set $A\subset{\mathbb{R}}$, $$|A(A+A)|\gg{|A|^{\frac{3}{2}+\frac{1}{178}}},$$ giving a partial answer to a conjecture of Balog. In a similar spirit, it is established that $$|A(A+A+A+A)|\gg{\frac{|A|^2}{\log{|A|}}},$$ a bound which is optimal up to constant and logarithmic factors. We also prove several new results concerning sum-product estimates and expanders, for example, showing that $$|A(A+a)|\gg{|A|^{3/2}}$$ holds for a typical element of $A$.Comment: 30 pages, new version contains improved exponent in main theorem due to suggestion of M. Z. Garae