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Unformatted text preview: Examples 1. Karen has $200 and is saving up to buy the iPhone 5 next year. She can invest in two different assets: Asset A will give a return of 8% with probability 0.41, or a return of 3% with probability 0.59, while Asset B will give a return of 5% with probability 1. She will invest k % of her money in Asset A , and the remaining (1- k )% in Asset B . Karen’s utility function is given by ν ( w ) = ln w for w > 0. 1.1 Describe the main properties of this utility function (i.e. preferences, risk aversion) 1.2 How should Karen invest her money if she wants to maximise her utility? 2. Michel currently has $100. She will spend $ c today, and $(100- c ) R in one year’s time, where R ∼ ( Exponential with mean 1.12 with probability 0.6 Poisson with mean 1.1 with probability 0.4 . If Michel’s utility function is ν ( c ) = c- . 001 c 2 , determine her optimal spending at time 0. UNSW Week 8 ACTL1001 Tutorial Examples 3. Danny wants to insure his playing cards. The probability that they will be damaged during the next year is 0.1. Given that his cards get damaged, he will incur a loss of $10 with probability (w.p.) 0.7, $100 w.p. 0.2, or $1000 w.p. 0.1. 3.1 Determine the distribution of X , the unconditional loss, and show that E[ X ] = $12 . 7 , E[ X 2 ] = $10207 3.2 Simon offers Danny a complete insurance policy, charging an Esscher premium with h = 0 . 0001. Show that the premium is P = $13 . 75431638. 3.3 Suppose that Simon changes the insurance policy so that if Danny’s cards are damaged, then Simon will pay α % of the loss to Danny, in exchange for a premium of α P . Simon’s utility function is ν ( w...
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.
- One '09