1- An agent, with wealth 50, faces a probability 0.2 of a loss 35. The agent is offered insurance at a premium rate of 0.25. The agent has the von Neumann-Morgenstern utility function, u=lnx, where x is wealth. How much insurance should the agent buy?
2 - Show that a risk averse agent offered terms worse than actuarially fair will not choose to insure fully?© BrainMass Inc. brainmass.com October 24, 2018, 11:07 pm ad1c9bdddf
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An agent, with wealth 50, faces a probability 0.2 of a loss 35. The agent is offered insurance at a premium rate of 0.25. The agent has the von Neumann-Morgenstern utility function, u=lnx, where x is wealth. How much insurance should the agent buy?
Suppose the risk cover is L. Then the agent will choose the risk cover such that his expected utility is maximized.
The wealth because of the insurance contract is as follows
In the event of no actual loss
y1= 50-0.25*L ---------Equation 1
In the event of actual loss
y2= 50-35+L-0.25*L = 15+0.75*L ----------Equation 2
Since the probability of loss is 0.2, the expected utility from the two states will be ...
Shows mathematically and in simple English how a risk averse decision maker will take a decision to insure.
Individual purchasing insurance
In state of nature 1 the individual has income w, whereas in state of nature 2 the individual's income is y < w. The probabilities that these states will occur are (1 - p) and p, respectively. The individual can purchase insurance before the state of nature is known; an increase in income of s in state 2 can be purchased by a reduction in income of ∏s in state 1. Prove that a risk-averse von Neumann-Morgenstern individual will over-insure, fully-insure, or under-insure according as the insurance is available at a price ∏ lower than, equal to, or higher than the actuarially fair price.
∏ - symbol piView Full Posting Details