In this paper I prove a theorem that establishes bounds on the marginal rate of substitution between losing $x and winning $y, starting from wealth level $w for a risk averse individual that rejects a small stake gamble for a range of initial wealth levels. I am then able to prove a theorem that...

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agentacute;s payoffs or beliefs and...

For each individual with von Neumann and Morgernstern's preferences and for each gamble that can take negative values yet has positive expected value we calculate separately the reservation values of the losses and of the gains of the gamble and denote those values by risk and reward,...