Title: Pricing a guaranteed minimum maturity benefit in uncertain markets

Authors: Justin Chirima; Frank Ranganai Matenda; Mabutho Sibanda

Addresses: Department of Mathematics and Computer Science, Great Zimbabwe University, P.O. Box 1235, Masvingo, Zimbabwe ' School of Accounting, Economics and Finance, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag X54001, 4000, Durban, South Africa ' School of Accounting, Economics and Finance, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag X54001, 4000, Durban, South Africa

Abstract: This paper examines the problem of pricing a guaranteed minimum maturity benefit (GMMB) in uncertain markets. Several uncertainties are encountered in financial markets. The pricing process of a GMMB does not exhibit randomness alone, but also non-random uncertainties. We introduce uncertainty theory into pricing a GMMB. The assumption is that the stock price process, S_t, interpreted as an index for the fund assets, is driven by an uncertain differential equation (UDE). The solution to this UDE is regarded as a geometric canonical Liu process. We apply the UDE in pricing the GMMB problem and assume that the stock price evolution is driven by the canonical Liu process. Utilising the uncertain Liu option pricing approach, we formulate and examine a framework for pricing a GMMB in uncertain markets. Numerical computations are exemplified as well. The results of the study show that this approach is capable of pricing a GMMB.

Keywords: uncertainty; uncertainty distribution; canonical Liu process; guaranteed minimum maturity benefit; GMMB; insurance policyholders; stock price.

DOI: 10.1504/IJMOR.2025.145755

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.3, pp.295 - 307

Received: 10 Jul 2023
Accepted: 02 Aug 2023
Published online: 23 Apr 2025 *

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