Best Perplexity prompts for Actuaries

Assume a life insurance policy with a face value of $100,000 and a premium payment of $500 per year. Using the Society of Actuaries' (SOA) 2019 Valuation Basic Table (VBT) and assuming a 3% annual interest rate, calculate the policy's liability under different mortality rate scenarios (e.g., 90%, 95%, and 100% of the VBT rates). Provide a detailed breakdown of the calculations, including the present value of future benefits and expenses, and analyze the results to determine the most sensitive scenario. Consider the impact of changes in mortality rates on the policy's cash flows and reserves.

Develop a catastrophe bond pricing model using a stochastic process to simulate potential losses from natural disasters (e.g., hurricanes, earthquakes). Assume a bond with a principal amount of $10 million, a coupon rate of 5%, and a maturity of 5 years. Using historical data on catastrophe losses and a probability distribution (e.g., lognormal), estimate the expected loss and standard deviation of the bond's return. Provide a detailed description of the model's assumptions, limitations, and results, including the bond's price and yield under different scenarios.

Analyze the funding status of a defined benefit pension plan with 1,000 participants, assuming a plan asset value of $50 million and a liability of $60 million. Using the Pension Protection Act of 2006 (PPA) funding rules and assuming a 7% annual rate of return on plan assets, calculate the plan's funding shortfall and required contributions over the next 5 years. Consider the impact of different investment return scenarios (e.g., 5%, 7%, and 9%) on the plan's funding status and provide a detailed breakdown of the calculations, including the present value of future benefits and expenses.

Assume an insurance company with a total asset value of $1 billion and a liability of $800 million. Using the National Association of Insurance Commissioners' (NAIC) risk-based capital (RBC) framework and assuming a company action level (CAL) of 200%, calculate the company's regulatory capital requirement under different scenarios (e.g., 90%, 100%, and 110% of the CAL). Provide a detailed description of the RBC framework, the company's risk profile, and the calculations, including the determination of the company's authorized control level (ACL) and the calculation of the RBC ratio.