Economics Insights @ CBS

Recent papers have shown that Π^∞_{k = 1} P(k) = lim_m→∞ (P(m) ... P(1)) exists whenever the sequence of stochastic matrices {P(k)}^∞_{k = 1} exhibits convergence to an aperiodic matrix P with a single subchain (closed, irreducible set of states). We show how the limit matrix depends upon P(1).

For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation.

The article presents several lender supply and borrower demand conditions for a leverage structure of interest rates. The paper presents a model of the credit transaction between individuals embedded in a competitive credit market. In this model, the individual has to decide on the optimal allocation of his initial investible capital K, among a risk asset with random rate of return R-1 available to all investors, a riskless asset with return s-1 and lending to or borrowing from another individual. Short sales of the risk asset are not permitted.