Simple probability question Utility curve of an individual i

Simple probability question

Utility curve of an individual is exponential with Risk Tolerance = 4000 Consider the gamble that the individual wishes to play. There is no cost to play the gamble. Find EU, CE and Risk premium if the net worth of the individual before the gamble is a $10,000 and $20,000. Comment on the comparison between the Risk premium obtained from a) and b)

Solution

EU = ( 10000 * 0.4) + ( 5000 * 0.3) + ( 2000 * 0.3) = 6100

RISK PREMIUM for (a) = ( 6100+ 4000) - 10000 = 100......= 1 %

CE for (a) = 6100 / (1 + 1) = 3050......

RISK PREMIUM for (b) = ( 6100+4000) -20000 = -9900........ = - 49.5%
CE for (b) = 6100 / ( 1 - 49.5) = -125.7732..

comment : in a) certainty equivalent is 3050 and original value = 10000 and expected return was 6100 , so , there is no need to gamble practically!
but , this is a much better situation than (b).
where a negative C.E appears , that indicates that you are overbetting! and won\'t get anything!
so, this is a extreme situation , where , the gambling is not even a opTion!