Some risk processes associated to the debt function of a loan with variable interest rates

In previous work (reference 1), a risk random variable was introduced as the norm in a suitable space, of a stochastic process associated to the debt function of a loan. Some of the properties of the risk random variable were studied. In particular, under the hypothesis of interest rate constant in time, a simple condition on the debt function of the loan was shown to be sufficient in order to have control on the distribution function of the risk of the loan. In the following, we present some generalizations of those previous results, under the hypothesis of having the evolution of interest rates modelled by a known stochastic process.