Application of the Extended Gompertz Model in Analyzing Insurance Growth
The South African insurance sector is experiencing a positive growth as the nation is on high quality economic growth and development. However, there is little attention with regards to research on the growth analysis, hence the researchers aim to bridge the gap by analyzing the growth using a mathematically based approach. To verify the wide spread phenomenon behind insurance growth an extended Gompertz model (EGM) which is a member of the unified Richards family was used. The quantitative approach by means of functional limits, the cumulative distribution approach, initial value problem (IVP) and the qualitative derivative approach were used to fully analyze the model. We managed to derive a cumulative function was derived which can be used to estimate the number of insurance growth indicators.
The maximum carrying capacity of an insurance industry was estimated using the IVP which in our case is time dependent hence does not concur with other Gompertz related works. Using both the qualitative and derivative approach, a growth function which produced the same pattern with the original Gompertz curve with K(t) as the asymptotically stable and non-constant growth limit were deduced. Hence we can conclude that the growth of insurance sectors does follow a sigmoid shape with non-constant maturity levels. Lastly, we performed a statistical analysis of the nexus between insurance sector growth and economic development using GDP and insurance indicators (net premiums) data. From the statistical analysis done the results showed a positive relationship between the two. This showed that, insurance sector indeed plays a significant role towards economic development and as such their growth patterns should be well attended.
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