Actuarial valuation under interest rate uncertainty via $A$-linearly correlated fuzzy processes

Articles in Press

Document Type : Research Article

Authors

Institute of Applied Social Sciences, Federal University of Alfenas, Varginha, Minas Gerais, Brazil

Abstract

Interest rate assumptions play a fundamental role in actuarial valuation, since even small variations may significantly affect premiums and benefits. In many practical situations, however, interest rate uncertainty is epistemic rather than stochastic, arising from imprecision in expert judgment and incomplete market information. To address this issue, this paper applies the theory of $A$-linearly correlated fuzzy processes (fuzzy processes in which the dependence structure is governed by a linear correlation-type operator $A$ acting on fuzzy-valued functions) to the valuation of life insurance contracts. The contracted benefit is modeled as a fuzzy number, leading to a fuzzy present value represented by a fuzzy initial value problem with an explicit analytical solution. The $A$-linearly correlated fuzzy process is formally defined and employed to characterize the dependence structure underlying the fuzzy present value. By interpreting this value as a fuzzy function of the insured's lifetime, a closed-form expression for the fuzzy actuarial present value is derived through $\alpha$-level sets. It is shown that the resulting actuarial present value is a triangular fuzzy number whose bounds coincide with the classical actuarial present values obtained under extreme deterministic interest rate scenarios. The proposed framework provides a transparent and computationally efficient way to quantify the impact of interest rate imprecision on premiums and benefits, complementing traditional actuarial models without requiring probabilistic assumptions.

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Journal of Mathematical Modeling

Articles in Press, Corrected Proof
Available Online from 02 June 2026

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