ARM-BREAKING, CONSUMER CREDIT AND PERSONAL BANKRUPTCY

The consumer credit transaction is analyzed as a contract which provides insurance as well as present consumption for the borrower. Creditors' remedies such as "arm-breaking" are shown to facilitate provision of insurance (forgiveness of debts) when lenders cannot monitor outcomes. Alternatively, if outcomes are observable but lenders do not ex ante know the risk associated with each borrower, the market may generate an excessive amount of arm-breaking and agreements to forgo discharge following bankruptcy as low risk borrowers signal their characteristics, suggesting that government limitations on such provisions might be efficient. The secured credit transaction is shown to be a complex contract which attempts to provide efficient repayment, seller incentives for performance and mitigation following default, and insurance for the borrower. Garnishment and discharge of debts following bankruptcy are also considered.     

Penalized Maximum Likelihood Estimator for Normal Mixtures

The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in penalizing the likelihood function. The resulting penalized likelihood function is then bounded over the parameter space and the existence of the penalized maximum likelihood estimator is granted. As original contribution we provide asymptotic properties, and in particular a consistency proof, for the penalized maximum likelihood estimator. Numerical examples are provided in the finite data case, showing the performances of the penalized estimator compared to the standard one.     

Stochastic Differential Mixed-Effects Models

Abstract.  Stochastic differential equations have been shown useful in describing random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating random effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simultaneous representation of randomness in the dynamics of the phenomena being considered and variability between experimental units, thus providing a powerful modelling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies. In most cases the likelihood function is not available, and thus maximum likelihood estimation of the unknown parameters is not possible. Here we propose a computationally fast approximated maximum likelihood procedure for the estimation of the non-random parameters and the random effects. The method is evaluated on simulations from some famous diffusion processes and on real data sets.