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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 2152189, 14 pages
Research Article

Loan Transactions with Random Dates for the First and Last Periodic Instalments

Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano s/n, 04120 Almería, Spain

Received 9 March 2016; Accepted 11 July 2016

Academic Editor: Chin-Chia Wu

Copyright © 2016 María del Carmen Valls Martínez and Salvador Cruz Rambaud. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Usually, loan transactions contracted in practice are nonrandom; that is to say, all amounts received (principal) and paid (period instalments) by the borrower are previously agreed with the lender, as well as their respective dates. In this paper, two new alternative loan models are introduced, depending on whether the borrower survives or not to fulfil all repayment obligations. In this way, either the initial or the final date of repayments can be subject to this contingency. Additionally, the different parameters of such random transactions are determined, as well as several measures of profitability/cost for the lender/borrower, respectively. These transactions can be attractive for both the lender and the borrower, which therefore make them worthy of consideration and subsequent implementation for the benefit of both parties.