Abstract
The objective of this research is to consider varying unemployment duration in the pricing of unemployment insurance with application to USA data. The study assumes that unemployment duration follows Burr XII mixture distribution while the discount rate to use in the pricing of the scheme will bedetermined by fitting market data into the capital asset pricing model. The Burr XII mixture distribution has been used to model unemployment duration in order to allow for heterogeniety in the unemployment duration of the insured employees. The results yield a mean unemployment duration of approximately 16 weeks and premium contribution rate of 5.10% of the taxable wage base per month for a benefit of 45% of the taxable wage base per month payable on weekly basis during spells of unemployment.
Highlights
Pricing an insurance cover using discounted cash flow technique involves determining the timing, amount and probability of payment of cash flows together with the discount rate before applying the discounting formula
McDonald and Butler [10] noted that Weibull distribution assumes homogeneity in unemployment duration data which may lead to erroneous results
This is an improvement of the existing work by Beenstock [2] where unemployment risk is undiversified and an appropriate riskadjusted interest rate is specified for the unemployment insurance
Summary
Pricing an insurance cover using discounted cash flow technique involves determining the timing, amount and probability of payment of cash flows together with the discount rate before applying the discounting formula. This paper seeks to improve the model of Chuang and Yu [6] by incorporating the findings in the model by McDonald and Butler [10] This will be achieved by randomizing the scale parameter of the Weibull to form a mixture of the Weibull distribution. According to Malinvaud [9], unemployment insurance is a ‘special caseof insurance contract in that in most cases, it is compulsory and is wholly operated by the government In such a set-up, unemployment insurance is considered as a social program whose main goal is to provide unemployment benefits to partially replace lost earnings for previously. Richard Onyino Simwa et al.: Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data working individuals who become involuntarily unemployed that is, they are able, available and actively seeking for employment. This approach may not be consistent with reality since it does not account for the level of risk a worker is exposed to
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