Pricing a guaranteed minimum maturity benefit in uncertain markets

Justin Chirima, Frank Ranganai Matenda and Mabutho Sibanda

International Journal of Mathematics in Operational Research, 2025, vol. 30, issue 3, 295-307

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. (search for similar items in EconPapers)
Date: 2025
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