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Use of two valuation functions in ﬁnancial and actuarial transactions

Rambaud S. C., Valls M. C.

Control and Cybernetics

2016

Vol. 45, no. 1

111--124

Usually a ﬁnancial transaction is being considered with a single valuation function, but sometimes, and depending on the economic context, it is necessary to use one function to value the set of incoming payments and another to assess the set of outgoing payments. This paper, therefore, sets out to demonstrate that those ﬁnancial transactions which use two valuation (capitalization or discount) functions can be treated in the same way as those valued with a single valuation function in which some incoming or outgoing payments are random. Our methodology is applied to determine the periodic amounts necessary to reach a target capital at a certain point in the future time in two situations, namely when the withdrawal of the capital depends on the investor’s survival, and when the receipt of the capital (by the investor or his/her beneﬁciaries) is assured.