Time varying or static cut-offs for credit scorecards

This note points out that the ability of credit scorecards to separate Goods from Bads changes over time. A simple way of dealing with such changes is to adjust the cut-off scores being used. These adjustments can be made by using the score to log odds relationship which is regularly monitored. In a case study there are decreases in the costs—in some case considerable decreases—of using the scorecard by making such adjustments compared with making no adjustments.     

Monetary and relative scorecards to assess profits in consumer revolving credit

This paper presents for the first time a relative profit measure for scoring purposes and compares results with those obtained from monetary scores. The suggested measure is the cumulative profit relative to the outstanding debt. It can also be interpreted as the percentage coverage against default. Monetary and relative measures are compared with both being estimated using direct and indirect methods. Direct scores are obtained from borrower attributes, while indirect scores are predicted using the estimated probabilities of default and repurchase. Results show that specific segments of customers are profitable in both monetary and relative terms. The best performing indirect models use the probabilities of default within 12 months on books. This agrees with existing banking practice of default estimation. Direct models outperform indirect models. Relative scores would be preferred under more conservative standpoints towards default because of unstable conditions and if the aim is to penetrate relatively unknown segments. Further ethical considerations justify their use in an inclusive lending context.     

Cooperation in bike racing—When to work together and when to go it alone

We present an agent‐based model of bicycle racing that incorporates both physiology and the types of multiplayer scenarios that arise in real races. In these scenarios, riders can choose to share the workload with other riders (cooperate) or pursue their own self‐interests (defect). We compare the model's predictions to race situations and use it to investigate how different strategies can affect outcomes. We find that an individual player's best strategy depends on fitness level: below‐average riders fare better as defectors whereas above‐average riders perform better as cooperators. The strategies of stronger riders affect their teammates' results as well. The teammates of defecting strong riders fare worse overall than the teammates of cooperating strong riders. These results reproduce a dynamic that played out in the 2009 Tour de France. The winner, Alberto Contador, pursued a strategy perceived by many to be unusually uncooperative by repeatedly defecting on his teammates. The strategy worked to his advantage but may have negatively affected his teammates' placements. © 2011 Wiley Periodicals, Inc. Complexity, 17,39–44, 2011     

When graded domains are Schreier or pre-Schreier

We characterize, in terms of properties of homogeneous elements, when a graded domain is pre-Schreier or Schreier. As a consequence, the following properties of a commutative monoid domain A[M] are equivalent: (1) A[M] is pre-Schreier; (2) A[M] is Schreier; (3) A and M are Schreier. This is in contrast to pre-Schreier monoids and pre-Schreier integral domains, which need not be Schreier.     

When a line graph associated to annihilating-ideal graph of a lattice is planar or projective

Let (L,∧, ∨) be a finite lattice with a least element 0. AG(L) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L, and two distinct vertices I and J are adjacent if and only if I ∧ J = 0. We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by L(AG(L)), is a planar or projective graph.     

The facility location problem when the underlying distribution is either dominated or dominating

The theory of choices involving Risk is used to solve some classes of the Today maximin and minimax one facility location problems. Solutions are shown when the underlying demand distribution is symmetric and unimodal.     

When almost multiplicative morphisms are close to homomorphisms

It is shown that approximately multiplicative contractive positive morphisms from (with dim ) into a simple -algebra of real rank zero and of stable rank one are close to homomorphisms, provided that certain -theoretical obstacles vanish. As a corollary we show that a homomorphism is approximated by homomorphisms with finite dimensional range, if gives no -theoretical obstacle.

     

When nonautonomous equations are equivalent to autonomopus ones

We consider nonlinear systems of first order partial differential equations admitting at least two one-parameter Lie groups of transformations with commuting infinitesimal operators. Under suitable conditions it is possible to introduce a variable transformation based on canonical variables which reduces the model in point to autonomous form. Remarkably, the transformed system may admit constant solutions to which there correspond non-constant solutions of the original model. The results are specialized to the case of first order quasilinear systems admitting either dilatation or spiral groups of transformations and a systematic procedure to characterize special exact solutions is given. At the end of the paper the equations of axi-symmetric gas dynamics are considered.