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Chapter 0 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- Questions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.arrow_forwardPlease type out answerarrow_forwardPlease type out answerarrow_forward
- Please type out answerarrow_forwardUsing f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning. Please type out answerarrow_forwardThe function f(x) = log x is transformed to produce g(x) = log (x) – 3. Identify the type of transformation and describe the change. Please type out answerarrow_forward
- Each graph below is the graph of a system of three linear equations in three unknowns of the form Ax = b. Determine whether each system has a solution and, if it does, the number of free variables. A. O free variables ✓ B. no solution C. no solution D. no solution E. 1 free variable F. 1 free variablearrow_forward+ Find the first five non-zero terms of the Taylor series for f(x) = sin(2x) centered at 4π. + + + ...arrow_forward+ + ... Find the first five non-zero terms of the Taylor series for f(x) centered at x = 4. = 1 x + + +arrow_forward
- Questions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.arrow_forward7. 11 m 12.7 m 14 m S V=B₁+ B2(h) 9.5 m 16 m h+s 2 na 62-19 = 37 +, M h² = Bu-29arrow_forwardFind the interval and radius of convergence for the given power series. n=0 (− 1)" xn 7" (n² + 2) The series is convergent on the interval: The radius of convergence is R =arrow_forward
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