Unformatted text preview: choose? Justify your choice. 3. A decision maker’s utility function is given by u ( w ) =-e-. 002 w ,w > 0. The decision maker has an initial wealth of w = 5 , 000 and faces a random loss X with a uniform distribution on (0 , 5000). What is the maximum premium this decision maker will pay for a coinsurance which reimburses 80% of the incurred loss? 4. An individual has the following utility function: u ( w ) = w 1-γ 1-γ , w > (a) State the additional condition(s) so that the above utility function can be used to describe a risk-averse agent. (b) Now assume that the X follows a lognormal distribution with mean μ and variance σ 2 ; i.e. log X ∼ N ( μ,σ 2 ) , where N ( μ,σ 2 ) denotes the normal distribution with mean μ and variance σ 2 . Show that the certainty equivalent of X is CE = e μ + σ 2 2 (1-γ ) . Hint: use moment generating function of a normally distributed random variable....
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- Spring '10
- Normal Distribution, Probability theory, probability density function