[Consider a Bayesian decision problem in which F is the prior distribution over some parameter space T. If —ψ(d, t) is the product of the loss function and the likelihood function, then the Bayesian solution, d_F, maximizes extlesstex-math extgreater$E_\F\(d)= extbackslashint _\T\ extbackslashpsi (d,t)dF(t)$ extless/tex-math extgreater. Suppose \F^n\ is a sequence of distribution functions that approach F^0 in the sup-metric topology. Our main theorem gives conditions under which extlesstex-math extgreater$d_\F extasciicircum \\ extbackslashrightarrow d_\F extasciicircum\0$ extless/tex-math extgreater and extlesstex-math extgreater$E_\F extasciicircum\0\\(d_\F extasciicircum \\) extbackslashrightarrow E_\F extasciicircum\0\\(d_\F extasciicircum\0\\)$ extless/tex-math extgreater.]

[This paper considers the possibility of extending the Arrow-Pratt results on risk aversion to cases in which initial wealth is random. Specifically, we consider a situation in which an individual's wealth is the sum of two independent random variables extbackslashtilde\x\ and ỹ. We define the risk premium π( extbackslashtilde\x\, ỹ) which represents the reduction in mean wealth an individual is willing to accept to eliminate the random variable x̃ while retaining the random variable ỹ. It is shown that if u_1 is uniformly more (Arrow-Pratt) risk averse than u_2 and if either u_1 or u_2 exhibit nonincreasing (Arrow-Pratt) risk aversion, then extlesstex-math extgreater$ extbackslashpi _\2\( extbackslashtilde\x\, extbackslashtilde\y\)$ extless/tex-math extgreater is always smaller than extlesstex-math extgreater$ extbackslashpi _\1\( extbackslashtilde\x\, extbackslashtilde\y\)$ extless/tex-math extgreater. An example is given in which both u_1 and u_2 exhibit increasing risk aversion and in which this result fails.]