Loan transactions associated to continuous distributions of capital

The objective of this paper is to design a loan repayment plan adapted to the financed company with the aim to avoid a possible situation of illiquidity. More specifically, in this paper the sequence of payments which amortizes a loan is determined according to the distribution of the future income expected by the borrower. To do this, we will start from the concept of a continuous distribution of capital or, equivalently, a continuous annuity. The continuous distribution of capital will be derived from a continuous distribution of probability, to then obtain a discrete annuity which fits the future income of the debtor. On the other hand, it is noteworthy the analysis of the particular case of financial transactions with interest periods of different amplitude, which can facilitate the adjustment of the sequence of instalments to the timing of the real income of the borrower in loan transactions.