The assets and liabilities of a general insurance underwriter constitutes two main variables usually adopted when evaluating the solvency requirements of a general insurance firm under which technical provisions form an unprecedented part of insurance liabilities. The technical provision of a general insurance business comprises provisions for unearned premiums and provisions for claims. The technical provisions specified under solvency II requirements asserts that the classical actuarial techniques for evaluating the best estimate for provisions in general business insurance obligations contains the run off triangles. The objective of this study are to (i) estimate the chain ladder reserve (ii) estimate the cape-cod reserve and (iii) compare the chain ladder with the cape-cod mathematical techniques with the disposition of estimating losses and technical provisions. These techniques evaluated through some run-off triangles can be adopted to estimate technical provisions for the outstanding claims. Computational evidence from our results over the periods considered revealed that despite the fact that the cape-cod technique is a mathematical variant of the chain ladder technique which seems less dependent on the variations of a single observation, the chain ladder reserve is numerically less than the corresponding cape-cod reserve and hence CLRESERVE = 18534.42 < CCRESERVE = 19123.84

The aim of this paper is to describe a non-parametric technique as a means of estimating the instantaneous force of mortality which serves as the underlying concept in modeling the future lifetime. It relies heavily on the analytic properties of life table survival functions 𝒍𝒙+𝒕. The specific objective of the study is to estimate the force of mortality using the Taylor series expansion to a desired degree of accuracy. The estimation of the continuous death probabilities has aroused keen research interest in mortality literature on life assurance practice. However, the estimation of 𝝁𝒙 involves a model dependent on deep knowledge of differencing and differential equation of first order. The suggested method of approximation with limiting optimal properties is the Newton’s forward difference model. Initiating Newton’s process is an important level in terms of theoretical work which produces parallel results of great impact in the study of mortality functions. The paper starts from an assumption that 𝒍𝒙 function follows a polynomial of least degree and hence gives an answer to a simple model which overcomes points of singularity. Keywords: polynomials, contingency, analyticity, basis, differential, mortality, modeling

This paper aims at deriving actuarial modelling of equilibrium condition in life and pension mathematics under the framework of integral transform. The specific objective is to establish net actuarial balance representing the difference between the present values of contributions and benefit outgo of the defined benefit scheme. This is the equilibrium position such the plan sponsor cannot borrow to pay plan members at the point of retirement. Our investigation confirms that the present value of benefit outgo payable by the trustees equals the present value of total contribution of the plan sponsor so that the equilibrium point is reached under the framework of integral transform. Keywords: Integral transform, defined benefit, force of interest, equilibrium Fredholm, liability and Thiele

The international accounting standards  employee benefits describe the accounting requirements for employee’s short-term, post-retirement, long-term and termination benefits. It further enshrines the principle that the cost of providing employee benefits should be recognized in the period over which benefits are earned by the employee and defines how each cohort of employee benefit is estimated. The objectives of this study are: (i) to estimate the liabilities of each members of the scheme under  model (ii) to establish the mathematical condition under which the funding standard liability will be zero. This study applies the funding standard models for the computations of accruing liabilities for the current and past service liability of employees. Data in respect of different categories of employees was collected from a government institution in Jos North local government of Plateau state, Nigeria. The data includes the employee’s annual salary and their respective demographic statistics. This was used to obtain the number of years of pensionable service completed and the future years of services to be completed before retirement at the age of years. The study further employs life annuity table to compute the service liability of each member of the scheme. From our results, computational evidence proves that the total service liability of the plan will be vanishingly zero when certain mathematical annuity assumptions are imposed and hence this represents the condition for which the liability of the plan to the members to be zero.

Pension valuation exercises for a defined benefit scheme requires an appraisal of both the schemes assets and its liabilities in different circumstances. The valuations are required to comply with regulatory standards, most notably the minimum funding standard. The objectives of this study are: (i) to compute the estimate of minimum funding standard of pension liability (ii) to establish the actuarial condition under which minimum funding standard liability will be zero. This study used minimum funding standard models for the computations of accruing liabilities for the current and past service liability of employees. Data in respects of different categories of employees were collected over 36 employees from a going concern located in Jos South local government of Plateau State in Nigeria. The data includes the employee’s annual salary and their respective demographic data which includes sex, date of birth, date of employment. This was used to determine the number of years of pensionable service completed and the future years of services to be completed before retirement at the age of 65 years. The study also used life annuity table to compute the service liability of each member of the scheme. From the model used, the result shows that the total service liability of the plan will be vanishingly zero when the newly defined annuity component approaches zero hence this represents the condition for liability of the plan to the members to be zero.