Ana owns a car worth €50 000 which can get stolen with probability 1%. She can pur- chase coverage of the amount q = [0; 50 000] at premium 7 = €0.05 for each euro covered. Her utility function is u = In(w), where w is money. Assume she has no other assets. (a) Formulate her maximization problem. (b) How much insurance (9) will she choose to buy? Explain. (c) How much profits does the insurance company earn on insuring Ana?
Ana owns a car worth €50 000 which can get stolen with probability 1%. She can pur- chase coverage of the amount q = [0; 50 000] at premium 7 = €0.05 for each euro covered. Her utility function is u = In(w), where w is money. Assume she has no other assets. (a) Formulate her maximization problem. (b) How much insurance (9) will she choose to buy? Explain. (c) How much profits does the insurance company earn on insuring Ana?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Exercise 3
Ana owns a car worth €50 000 which can get stolen with probability 1%. She can pur-
chase coverage of the amount q € [0; 50 000] at premium 7 = €0.05 for each euro covered.
Her utility function is u = ln(w), where w is money. Assume she has no other assets.
(a) Formulate her maximization problem.
(b) How much insurance (q) will she choose to buy? Explain.
(c) How much profits does the insurance company earn on insuring Ana?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3a2c62e-2563-433d-9c00-60342131942d%2Fd36bf6d6-e5b6-47aa-807f-dc018e07d406%2Fglkcyek_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 3
Ana owns a car worth €50 000 which can get stolen with probability 1%. She can pur-
chase coverage of the amount q € [0; 50 000] at premium 7 = €0.05 for each euro covered.
Her utility function is u = ln(w), where w is money. Assume she has no other assets.
(a) Formulate her maximization problem.
(b) How much insurance (q) will she choose to buy? Explain.
(c) How much profits does the insurance company earn on insuring Ana?
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