Decision-Making under Uncertainty by Tapan Biswas (auth.)

By Tapan Biswas (auth.)

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The first person is the insuree and the second person is the insurer. There are two possible states with probability p for the state two (state of accident) to occur. Both individuals agree on this probability. However, individual 1 can reduce the probability (p) by undertaking an expenditure (e). e. p = p(e) and p'(e) < O. The utility functions for these two individuals are state independent and are denoted by u and v for persons 1 and 2 respectively. The state-contingent endowments of these persons are given by [lfl(1), lfil)] for individual 1 and [lfl(2), lfi2)] for individual 2.

For quadratic utility functions, when W < b/c, the degree of absolute risk aversion increases asO W increases. This is somewhat counter intuitive. One expects that when a person gets rieher, his aversion to risk declines as in type (i) and type (ii) utility functions. This casts some doubt on the advisability of using quadratie utility functions in the context of uncertain prospects. The same can also be said about type (iv) utility functions commonly known as constant absolute risk aversion (CARA) utility functions.

We know from our discussion in Chapter 2 that the individual with v(w) as his utility function is more risk averse than the individual with the utility function u(w) for all values of w. As before, consider two lotteries LI and L 2 with corresponding probability density functionsj(w) and g(w). 3) may be interpreted as the condition for SSD in utility (Biswas, 1991). Let us examine this condition in detail. e. we can regard a lottery on wealth as a lottery on utility. Suppose the lotteries j(w) and g(w) induce lotteries s(u) and t(u) in the utility space.

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