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2. Suppose that C= 1 and l = 2. Assume that the ruin probabi...

2. Suppose that C= 1 and l = 2. Assume that the ruin probability is given by = 0.5e-0.7u , u > 0. (a) Find the adjustment coefficient s*. (b) Find the mean of the claims . (c) Find My (s*). (d) Is it true in general that My (s*) > u? Why or why not?

C1. Assume that W(t) is the standard Brownian motion. Calcul...

C1. Assume that W(t) is the standard Brownian motion. Calculate the probability that W (3) > W (2) > W (1). C2. (a) Using the moment generating function, find E[X4], where X is a standard normal random variable with mean 0 and variance o?. (b) Find E[(W(s))²(W(t))²], whe...

F1. Use risk-neutral valuation to find the value of European...

F1. Use risk-neutral valuation to find the value of European style option on non-dividend paying asset with lognormal price dynamics if the payoff of the option at maturity is equal to ((S(T))³ K)+. Finally, find a formula for the delta of this option. G1. Consider three securities with the ...

3. (8.6) You are given: Claims are reported at a Poisson ra...

3. (8.6) You are given: Claims are reported at a Poisson rate of 5 per year. The probability that a claim will settle for less than $100,000 is 0.9 What is the probability that no claim of $100,000 or more is reported in the next three years?

The solutions should be clearly written explanations, not ju...

The solutions should be clearly written explanations, not just numbers. Chapter 8: 5, 7, 8, 10, 14(n = 5), 16(n = 5). Problem: (a) Go to webpage http://finance.yahoo.com (or any other similar webpage) and you can get quotes (historical prices) for your favorite stock (e.g. MSFT is symbol for Mi...

. A1. (a) Find the moment generating function of a random v...

. A1. (a) Find the moment generating function of a random variable x ~ N(11,02). (b) Find E|x*] (c) For 0 and o = 1, find E[X|X > 0]. A3. If you play roulette 100 times, betting $100 on black each time, what is the probability of winning at least $1000, and what is the probability of los...

Problem D: Suppose that there are several risky securities a...

Problem D: Suppose that there are several risky securities and that their efficient frontier is given by a - 0.29 - 4 + 202. 1. What is the expected return and risk of the minimal variance portfolio? 2. Add a risk-less asset with return R = 7%. Find the expected return and risk of the market por...

Let us play a game of cards, shall we? I will be the dealer,...

Let us play a game of cards, shall we? I will be the dealer, you will do the betting. The rules are simple. I take a standard deck of 52 playing cards and shuffle it well. I begin to flip over the cards in the deck, in sequence, one at a time. Immediately before each flip, you have the opportunity t...

A2.The initial price of the stock is S0 = 17 and the price f...

A2.The initial price of the stock is S0 = 17 and the price follows the binomial model in which in each period the price can go up by the factor u or down by the factor d. The numbers u, d, and the interest rate r are not known to us. A company Not Very Smart Bank Made Solely for The Purposes of T...

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