A. [15 marks]
Sagicor Insurance just hired you as an intern in the Actuarial department. You noticed that the department
is assessing their risk profiles, however, it can be improved significantly. Now is your time to shine. A
summary of the entire 2380 policies and their claim history under the medical insurance scheme can be
seen below. Use the data to better model the frequency distribution function under the medical insurance
scheme.
Number of Accidents Number of Policies
0 1110
1 690
2 310
3 160
4 70
5 30
6 10
i) Prepare a presentation for your manager to circulate to the directors for approval. Try to ensure there is at least one visual for the board members to appreciate.
ii) During the presentation to the board members, the chairman insisted he wants to limit the number of possible claims for an individual to 3. From your model, what estimated percentage of the policies will be somewhat affected by this change.
iii) After the presentation, the board members commended you. However, they strongly believe that the risk associated with no claims needs to be changed because they will be decreasing the minimum deductible by 30% in 2023 to attract more customers. As such they believe customers will claim more and the probability for no claim will reduce by 40%. Advise them of the new
percentage of individuals that is likely to be affected with the deductible implementation, if
they maintain the policy of limiting individuals to 3 claims.
Students and doctors at the University Hospital of the West Indies are trying to assess the impact the latest Covid–19 vaccine boost is having on their recently changed cost budget of $500,000 per day for infected vaccinated citizens. Since the rollout of the booster shot, in any given week, they are seeing already vaccinated patients being hospitalized and tested positive again with the corona
virus now following a Poisson frequency distribution. Since the rollout of the booster shot, 2 vaccinated persons are tested positive on average during any given day in comparison to 4 unvaccinated persons being tested positive. When a vaccinated person is tested positive with the COVID–19, the cost amount to
the hospital has the following distribution:
X (‘000’) fX(x)
150 0.7
200 0.2
300 0.1
For vaccinated patients, during a given day:
• Calculate the expected aggregate cost
• Calculate the probability the total hospital cost for the day will meet the budget.
• Calculate the standard deviation of the total cost per day.
After you have learned Loss Models in school, you have been fascinated with the insurance industry and
decided to start an insurance company at Utech offering an elite insurance product, covering a rare item that
no other insurance company is covering. You did some research on the market with a similar product and
gather the following total claim data from your few policyholders:
X (‘thousand) 0 1 4 5
f(x) 0.6 0.3 0.05 0.05
The premium collected from all the policyholders is 1 thousand per school term and is paid at the end of
each term. You decided to start the business with two (2) thousand dollars.
Now that you are convinced that your model data is correct, you want to know the following:
a) What is the chance that your insurance business will fail one day?
b) You believe you will be migrating from Jamaica to America after the end of the next three (3) school
terms and hope the business will survive then. What are the chances that the business survives the
three (3) school terms when it is time to leave Jamaica?
c) You told yourself you want at least a 90% chance of survival eventually, estimate the initial capital
that would be needed to guarantee this. Approximate the adjustment coefficient using the
formula below (an approximation in the Actuarial text):
i) Is there a significant difference between the approximation of r* and the actual r*.
(Show working calculating the actual r*)
