Savings operations with random commencement and conclusion

The progressive aging of the population is suggesting that public pension plans should be increasingly supplemented by private savings schemes. Accordingly, this supposes the appearance of a wide range of innovative savings products to meet the varying needs of savers and financial institutions. In practice, most contracted savings operations are nonrandom, that is to say, all amounts involved in the transaction are sure as well as their respective maturities. Consequently, the purpose of this paper is to propose a savings operation which includes the randomness derived from the contingencies which suppose the eventual but unpredictable death of the saver and a person designated by him to receive the final agreed amount.

The methodology used in this paper is financial mathematics where the risk has been introduced as an element which defines the main characteristics of this novel saving operation.

The proposed model extends the range of savings products by describing an actual innovation with new practical applications with respect to the traditional models of saving. In this paper, the authors have proposed a new type of saving based on the contingency derived from the life expectancy of the saver, by raising an operation in which the commencement and conclusion of the savings period are random. These savings operations represent, undoubtedly, a novelty from a financial point of view.

The main added value of this paper is that these contingencies affect the periodic deposits in each period from the first to the last maturities of installments. Moreover, the different parameters of such random transactions are defined.