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All Journal Mikailalsys Journal of Mathematics and Statistics
Adebayo, Ajala Olusegun
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Engineering Mathematics Mechanical Engineering

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Quantitative Assessment of Interest Rate Fluctuation Sensitivity in Nigerian Insurance Asset-Liability Management Adewale, Taiwo Abiodun; Tinuoye, Oladipo Abiodun; Adebayo, Ajala Olusegun; Oluwaseyi, Olaiya Olumide; Olalekan, Owoade Olusegun; Damilare, Olaleye Peter
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.7182

Abstract

This study investigates the sensitivity of insurance portfolios to interest rate fluctuations in Nigerian insurance companies, with particular focus on the implications for asset and liability valuation. The objective is to assess how interest rate variability affects the relative sensitivities of assets and liabilities, and the resulting solvency risks. A quantitative approach was adopted, using a sample of ten insurance companies selected based on asset base and data availability. Data covering a ten-year period (2013–2023) were obtained from published financial statements and Central Bank of Nigeria interest rate bulletins. Analytical techniques included stochastic simulations and regression modeling, applying the Vasicek and Heston frameworks, with visualization performed using Python 3.12.3. The results show that liabilities exhibit greater sensitivity to interest rate fluctuations than assets, with pronounced volatility under stress scenarios, thereby creating significant solvency challenges. These findings validate the importance of dynamic stochastic models in capturing the complexities of interest rate effects, as opposed to static mathematical assumptions. The study concludes that effective asset–liability management (ALM) requires robust dynamic interest rate modeling. Theoretical contributions include extending the application of stochastic differential equations to emerging market contexts, while practical recommendations urge insurance regulators and investment managers to adopt interest rate-sensitive frameworks for risk management and capital adequacy assessments. Future research is recommended on macroeconomic stress factors and stochastic volatility models tailored to African financial markets.
An Improved Black–Scholes Model to Determine the Optimal Boundary of Asset–Liability Akintayo, Olajide Olatunbosun; Tinuoye, Oladipo Abiodun; Adebayo, Ajala Olusegun; Oluwaseyi, Olaiya Olumide
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.7218

Abstract

The study addresses limitations of the Black–Scholes framework, specifically its reliance on a risk-neutral market and a self-financing hedging portfolio by proposing a generalized derivative pricing approach grounded in the efficient markets hypothesis. The research objective is to establish a valuation model in which a derivative’s fair value equals a conditional expectation discounted at the underlying asset’s drift, thereby explicitly retaining the asset’s drift rather than abstracting it away under risk neutrality. Methodologically, the paper develops a partial differential equation (PDE) that replaces the risk-free rate with an efficiency-consistent discount rate, derives a pricing formula for European call options that incorporates the underlying’s drift, and analyzes the optimal exercise boundary for American call options under varying parameters. Key findings show that the optimal exercise price increases with higher volatility and risk-free interest rates and decreases with higher dividend yield; moreover, it is never optimal to exercise an American call option early when the underlying pays no dividends. The study concludes that an efficiency-based discounting scheme offers a coherent alternative to risk-neutral valuation while preserving internal consistency with observed market dynamics. The contribution and implication are a drift-inclusive theoretical framework that refines PDE-based pricing, clarifies comparative statics for exercise policy, and provides practitioners with guidance for pricing and exercise decisions in settings where asset drift is informationally relevant.
On the Closed-Form Characterisation of the Impact of Risk Misprofiling on Optimal Nigerian Insurance Pricing Models Adewale, Taiwo Abiodun; Tinuoye, Oladipo Abiodun; Adebayo, Ajala Olusegun; Oluwaseyi, Olaiya Olumide; Olalekan, Owoade Olusegun; Damilare, Olaleye Peter
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i1.7597

Abstract

This study addresses the underexplored issue of risk mis-profiling in optimal insurance pricing models and its implications for solvency and regulatory compliance within the insurance industry. It aims to mathematically analyse the effects of classification errors on premium determination, quantify pricing deviations, and assess sensitivity to misclassification biases. Adopting a quantitative research design, the study utilises insurance data spanning 2010–2020, with computational implementation in Python 3.12.3 (2025) and calibration in Weka 3.9.6 (2022). Policyholders were categorised into low-, medium-, and high-risk groups using confusion matrices, while premiums were derived under exponential utility and deterministic-equivalent principles. Analytical techniques included cumulant generating function expansions, Taylor–Lagrange remainder approximations, and optimisation frameworks. The results indicate that even minor classification errors significantly influence premium estimates, particularly due to exponential tilting, variance underestimation, and tail sensitivity. These distortions align with theoretical expectations and highlight solvency vulnerabilities when premiums fall below actuarially fair values. The study concludes that systematic mis-profiling introduces pricing inefficiencies and potential insolvency triggers. Theoretical contributions include the extension of utility-based pricing principles to account for classification uncertainty, while practical implications call for insurers and regulators to adopt robust pricing adjustments, monitor classifier accuracy, and integrate misclassification-aware pricing mechanisms. Future research directions include extending the framework to portfolio-level analysis, applying robust stochastic optimisation, and investigating the effects of machine learning classification errors on pricing precision.
Co-Authors Adewale, Taiwo Abiodun Akintayo, Olajide Olatunbosun Damilare, Olaleye Peter Olalekan, Owoade Olusegun Oluwaseyi, Olaiya Olumide Tinuoye, Oladipo Abiodun