1. Discuss the meaning of survival model. How would you use the cumulative distribution of a random variable to survival model.

2. The stock of company C is currently worth RS 100 per share. In one year, this price can either be RS 120 or RS 90. The company does not pay dividends on its stocks. The annual continuously compounded risk free interest rate is 5%. The strike price of a European call option on the company stock is RS 110. Using the one-period binomial option pricing model, find the price today of one such option on the company's stock.

3. List two widely used distributions to describe occurrence of extreme events. Give reasons in support of your choice and discuss their methods of estimation.

4.(a) Discuss the features of Buhlmann credibility theory.
The number of cars that crushes people in a year follows a Poisson distribution with mean A. The prior distribution of A is a gamma distribution with a=3 and 8=1.9. During a three year period you observed the people have been crushed by 2 cars in year 1 and 4 cars in year and 0 cars in year 3. Use Buhlmam, credibility to estimate the number of cars that will crush people in year 4.

5. Suppose that at^2 10B. If X is invested at time 0 (zero) accumulates to RS 500 at time 4 and to RS 1,000 at time 10, find the amount of the original investment X.

6. Consider an age-at-death random variable X with survival distribution defined by <img src='./qimages/9916-6.jpg'>


(a) Explain why this is a suitable survival function. Find the corresponding expression for the cumulative probability function. Compute the probability that a new born with survival function defined above will die between the ages of 65 and 75.

7. Consider the life table given as follows:

<br><br> <img src='./qimages/9916-7.jpg'> Find the number of individuals who die between ages 2 and 5. What is the probability of a life aged 2 to survive to age 4.

8. LLC company has a stock price of RS 555 per share. A replicating portfolio for a particular call option on LLC stock involves borrowing RS 56 and buying 3/4th of the one share. Calculate the price of the call option using the one-period binomial option pricing model.

9. The stock of company Black Berry currently sells for RS 1,500 per share. The annual stock price volatility is 0.2 and the annual continuously compounded risk-free interest rate is 0.05. The stock's annual continuously compounded dividend yield is 0.3. Find the value of d1 in the Black-Scholes formula for the price of a call option on Black Berry stock with strike price RS 1,600 and time to expiration of 3 years.

10.(a) Discuss the significance of individual risk model.
Life Insurance Corporation of India has insured 5 individuals with following
characteristics <img src='./qimages/9916-10b.jpg'>

Find the expected value of aggregate losses next year for this group of five life insurance policies.

11. John starts a gamble with RS 2 with probability of win p O.6 What is the probability that John obtains a fortune of N 4 without going broke? What is the probability that Johan will become infinitely rich? If John start with i 1 instead, what is the probability that he would go broke?

12. Why do you recommend the regulation of insurance industry by the government? Discuss the functional areas of the industry that require control in a regime of economic liberalization.