force of interest
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Risks ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 122
Author(s):  
Franck Adékambi ◽  
Kokou Essiomle

In this paper, we derive a closed-form expression of the tail probability of the aggregate discounted claims under homogeneous, non-homogeneous and mixed Poisson risk models with constant force of interest by using a general dependence structure between the inter-occurrence time and the claim sizes. This dependence structure is relevant since it is well known that under catastrophic or extreme events the inter-occurrence time and the claim severities are dependent.



2020 ◽  
Vol 39 (1) ◽  
pp. 15-24
Author(s):  
G.M. Ogungbenle ◽  
J.S. Adeyele

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



2020 ◽  
Vol 50 (1) ◽  
pp. 155-185
Author(s):  
Tzuling Lin ◽  
Cary Chi-liang Tsai

AbstractIn this paper, we first derive closed-form formulas for mortality-interest durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel movement, respectively, in μ* (the force of mortality-interest), the addition of μ (the force of mortality) and δ (the force of interest). We then build several mortality-interest duration and convexity matching strategies to determine the weights of whole life insurance and deferred whole life annuity products in a portfolio and evaluate the value at risk and the hedge effectiveness of the weighted portfolio surplus at time zero. Numerical illustrations show that using the mortality-interest duration and convexity matching strategies with respect to an instantaneously proportional change in μ* can more effectively hedge the longevity risk and interest rate risk embedded in the deferred whole life annuity products than using the mortality-only duration and convexity matching strategies with respect to an instantaneously proportional shift or an instantaneously constant movement in μ only.





2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qingwu Gao ◽  
Xijun Liu

The insurance risk model involving main claims and by-claims has been traditionally studied under the assumption that every main claim may be accompanied with a by-claim occurring after a period of delay, but in reality each main claim can cause many by-claims arriving according to a counting process. To this end, we construct a new insurance risk model that is also perturbed by diffusion with constant force of interest. In the presence of heavy tails and dependence structures among modelling components, we obtain some asymptotic results for the finite-time ruin probability and the tail probability of discounted aggregate claims, where the results hold uniformly for all times in a finite or infinite interval.



Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3243-3255
Author(s):  
Dawei Lu ◽  
Jiao Du ◽  
Hui Song

In this paper, a bidimensional renewal risk model with constant force of interest and Brownian perturbation is considered. Assuming that the claim-size distribution function is from the subexponential class, three types of the finite-time ruin probabilities under this model are discussed. We obtain the asymptotic formulas for the three types, which hold uniformly for any finite-time horizon.



Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 110 ◽  
Author(s):  
Sooie-Hoe Loke ◽  
Enrique Thomann

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.



2018 ◽  
Vol 13 (2) ◽  
pp. 1593-1608
Author(s):  
Bamidele Mustapha Oseni ◽  
Jolayemi Emmanuel Tejub


2017 ◽  
Vol 48 (1) ◽  
pp. 139-169 ◽  
Author(s):  
Katja Ignatieva ◽  
Andrew Song ◽  
Jonathan Ziveyi

AbstractThis paper introduces the Fourier Space Time-Stepping algorithm to the valuation of variable annuity (VA) contracts embedded with guaranteed minimum withdrawal benefit (GMWB) riders when the underlying fund dynamics evolve under the influence of a regime-switching model. Mortality risk is introduced to the valuation framework by incorporating a two-factor affine stochastic mortality model proposed in Blackburn and Sherris (2013). The paper considers both, static and dynamic policyholder withdrawal behaviour associated with GMWB riders and assesses how model parameters influence the fees levied on providing such guarantees. Our numerical experiments reveal that the GMWB fees are very sensitive to regime-switching parameters; a percentage increase in the force of interest results in significant decrease in guarantee fees. The guarantee fees increase substantially with increasing volatility levels. Numerical experiments also highlight an increasing importance of mortality as maturity of the VA contract increases. Mortality has less impact on shorter maturity contracts regardless of the policyholder's withdrawal behaviour. As much as mortality influences pricing results for long maturities, the associated guarantee fees are decreasing functions of maturities for the VA contracts. Robustness checks of the Fourier Space Time-Stepping algorithm are performed by making numerical comparisons with several existing valuation approaches.



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