Please do all 4 assignments attached
RMI 2101 Summer 2021 Homework Assignment 8 20 Points Be careful to follow the Guidelines for Homework Document & Directions for Turnitin on Canvas/Home/Course Documents. Show ALL of your work to receive full credit for an answer. 1. Song owns a $300K house and has a 10% chance of experiencing a fire in any given year. Assume that only one fire per year can occur and that if a fire occurs, the house is completely destroyed. Suppose that Song purchases a full insurance contract from Lemonade Insurance Company for an actuarially fair premium. This contract would pay all losses due to the fire. Assume that Song’s contract is the only insurance contract Lemonade Insurance Company sold. a. What is the probability distribution of total losses for Lemonade Insurance Company if they sell a contract to Song? (2 points) b. What is the actuarially fair premium [AFP] Lemonade Insurance Company will charge Song in the coming year? (1 point) c. What is the amount of risk Lemonade Insurance Company faces if they have Song as their only customer? (2 points) 2. Trevone, who owns the same type of house and faces the same probability distribution of losses as Song, also purchases full insurance for an actuarially fair premium from Lemonade Insurance Company. We assume that the two houses are independent of each other. In other words, if one house has a fire, this has no impact on the probability of the other house having a fire. a. What is the probability distribution of total losses for Lemonade Insurance Company if they sell contracts to both Song and Trevone? (2 points) b. What is the expected loss or expected payout for Lemonade Insurance Company if they sell contracts to both Song and Trevone? (1 point) c. What is the amount of risk Lemonade Insurance Company faces if they sell contracts to both Song and Trevone? (2 points) d. Briefly explain the benefit(s) to Lemonade Insurance Company as the number of insurance contracts sold increases? (2 points) 3. Now suppose Yu owns a $450K house and has a 10% chance of experiencing a fire in any given year. Assume as before that the fire will result in a total loss. Suppose the Lemonade Insurance Company offers Song and Yu the same insurance contract and charges them the same premium. In other words, they put Song and Yu into the same risk pool. a. What is the probability distribution of total losses for Lemonade Insurance Company if they sell contracts to Song and Yu? (2 points) b. What premium must Lemonade Insurance Company charge each of Song and Yu if they want to ‘break even’? (2 points) c. Will Song purchase this contract if he is charged the ‘break-even’ premium? Will Yu purchase this contact if he is charged the ‘break-even’ premium? Briefly explain your reason. (2 points) d. What is the amount of risk Lemonade Insurance Company faces if they sell contracts to both Song and Yu? (2 points) 4. BONUS: Compare the situation in question 2 and 3 above. In particular, examine the results you obtain in 1(c), 2(c) and 3(d). Explain carefully the ‘tradeoff’ that is illustrated. (4 points) RMI 2101 Summer 2021 Homework Assignment 7 20 Points Be careful to follow the Guidelines for Homework Document & Directions for Turnitin on Canvas/Home/Course Documents. Show ALL of your work to receive full credit for an answer. 1. Kimberly-Clark Company owns a warehouse worth $80,000. Ray Van Eperen is the risk manager. Kimberly-Clark faces the risk of fire which would completely destroy their warehouse. The probability of a fire is known to be 5%. Kimberly-Clark is considering the following risk management options to address the risk of fire to their warehouse: [1] Retention [2] Retention + Safety Program [3] Full Insurance (without Safety Program) for a premium of $4,600 The cost of the Safety Program is $2,800. It has the impact of lowering the probability of a fire from 5% to 2%. However, if a fire does occur it is still a total loss. a. Construct the loss matrix from Kimberly-Clark’s perspective. Make sure you show loss in the top row and out-of-pocket cost in the bottom row in each cell of the loss matrix. [2 points] b. Construct the payout matrix from an insurer’s perspective. [2 points] c. What is the actuarially fair premium [AFP] for full insurance? [1 point] Assume Ray’s worry value for retention without safety program (WVR) is $750 and his worry value for retention with safety program (WVRS) is $300. d. If Ray’s decision rule is to pick the option that minimizes TOTAL EXPECTED COST, what risk management option does he choose? Make sure that you consider all three options, clearly define TOTAL EXPECTED COST in each case and show all calculations. [2 points] e. What is Ray’s PMAX for full insurance without safety program as opposed to retention without safety? [1 point] f. During a meeting, the Chief Risk Officer (CRO) told Ray that the most he would pay for full insurance without safety program (as opposed to retention without safety) is $4,700. What is the CRO’s worry value for retention without safety program (WVR)? [1 point] g. Who is more risk averse, the CRO or Ray? Explain. [1 point] 2. Kramerica Company has a small plant worth $6,000. The plant is subject to physical damages and total destruction as a result of fire. From over 6,000 observations, the firm has derived the following probability distribution of fire losses for its physical plant. Loss Amount ($) Probability of Loss 0 0.92 2,500 ? 6,000 0.02 Kramerica is considering the following risk management options: [1] Partial insuranceFace Amount = $5,000; Premium = $330 [2] Deductible insuranceFace Amount = $6,000; Premium = $290; Deductible per occurrence = $1,000 [3] Full insurance Face Amount = $6,000; Premium = $360 a. Construct the loss matrix from Kramerica’s perspective. Make sure you show loss in the top row and out-of-pocket cost in the bottom row in each cell of the loss matrix. [2 points] b. Construct the payout matrix from an insurer’s perspective. [2 points] c. What is the AFP for deductible insurance in this case? [2 points] d. Assume that the company’s decision rule is to pick the option that minimizes TOTAL EXPECTED COST. Can you identify what risk management option is chosen? Why or why not? Make sure that you show all calculations and clearly define TOTAL EXPECTED COST in each case. [3 points] e. Assume that the company’s decision rule is to pick the option that minimizes TOTAL EXPECTED COST, what worry value(s) would make partial insurance preferred to full insurance? Show all work and calculations and explain your numerical answer. [1 point] RMI 2101 Summer 2021 Homework Assignment 9 24 Points 1. Matt works for Rowan University and has an annual income of $100,000. Assume Matt has a combined tax rate of 25%. In addition to salary, Matt receives health insurance, long term disability insurance and life insurance from Rowan as described below. Matt also has the opportunity to place funds into a dependent care flexible spending account. a. Rowan offers health insurance on a non-contributory basis. The premium is $6,000 per year. What would Matt’s total yearly income tax liability? (2 points) b. Matt decides to put $2,500 into a dependent care flexible spending account. What would be the total yearly income tax liability for Matt now? (2 points) c. If Matt should become disabled, he could no longer work for Rowan and would lose his $100,000 annual income. Suppose Rowan also offers long term disability insurance on a non-contributory basis. The premium is $3,000 per year. The long-term disability contract promises to pay Matt $80,000 per year should he become disabled. If Matt should become disabled at the beginning of the year, what would be his total yearly income tax liability? (3 points) d. Suppose Rowan offers long-term disability insurance described in (1c) on an employee pay all basis. Suppose Matt paid the entire premium cost of $3,000 per year using a pre-tax salary reduction arrangement. If Matt should become disabled at the beginning of the year, what would be his total yearly income tax liability? (3 points) e. Suppose Rowan offers long-term disability insurance described in (1c) on an employee pay all basis. Suppose Matt paid the entire premium cost of $3,000 per year using an after-tax salary reduction arrangement. If Matt should become disabled at the beginning of the year, what would be his total yearly income tax liability? (3 points) f. Matt also receives group term life insurance (GTLI) from Rowan on a non-contributory basis. The face amount of this GTLI policy is $90,000. This contract has a premium cost of $900 per year ($10 per $1000 of face amount). What impact will this have on Matt’s total yearly income tax liability? (3 points) 2. Joe has been working for Company A for a total of four years. Company A offers Joe a 401(k) plan. At the end of the fourth year of working at Company A, Joe leaves and begins working for another employer – Company B. Company B also offers a 401(k) plan. When Joe leaves Company A, his 401(k)-account balance is $96,000, of which: · Company A’s contribution = $60,000 · Joe’s contribution = $20,000 · Interest earnings = $16,000. a. Upon leaving Company A, how much of the 401(k)-account balance can Joe take with him at a minimum? (3 points) b. If Company A uses a three-year cliff vesting schedule, how much of the 401(k)-account balance can Joe take with him in total? (2 points) c. If Company A uses a graded 2-6 vesting rule, how much of the 401(k)-account balance can Joe take with him in total? (3 points) Be careful to follow the homework guidelines in order to maximize your score for this homework RMI 2101 Summer 2021 Homework Assignment 6 12 Points Hint: Read the questions carefully and be sure that what you write answers the questions. Many times students give correct information in an answer but that information is not the answer to the question. 1. Refer to the article in Topic 5 / Core Articles, “Insurers Are Going High-Tech to Mitigate Risk This Hurricane Season.” a. Indicate an example of a risk control option being discussed in this article. [2