problem 1) Describe the properties of exponential utility function.

problem 2) prepare a detailed note on optimal insurance

problem 3) Describe the basic aspects of models for individual claim random variables.

problem 4) Describe the survival function.

problem 5) Describe force of mortality and state its properties.

problem 6) Describe curate expectation of life.

problem 7)a) Describe the theory of utility as applied to insurance problems.

b) describe the elements of insurance.

problem 8)a) Describe the convolution method and the M.G.F. method for finding the distribution of the sum of independent random variables.

b) If X has uniform distribution on (0,2) and Y is independent of X with a uniform distribution over(0,3), find the distribution function of S=x+y by convolution.

problem 9)a) The force of mortality for survival model is μ(x) = 0.9/(90-x)for 0 ≤ x < 90

(i) Determine the survival function

(ii) Compute the approximate probability that a life aged 40 dies within next week.

b) Life time X of a newborn is exponentially distributed with mean life time of 65 years. Then,

(i) identify survival function

(ii) determine the probability that a new born is still alive at the age of 100.

(iii) determine the probability that a new born dies between the ages 50 and 65.

problem 10)a) Describe the laws of mortality.

b) Derive the relationship between life table functions and the survival functions.