In this paper we provide a novel family of stochastic orders, which we call the \alpha,[a,b] -convex decreasing and \alpha, a,b -concave increasing stochastic orders, that generalizes second order stochastic dominance. These stochastic orders allow us to compare two lotteries, where one lottery has a higher expected value and is also riskier than the other lottery. The main motivation for introducing the \alpha,[a,b] -convex decreasing stochastic orders is that they allow us to derive novel comparative statics results for important applications in economics that could not be derived using previous stochastic orders. In particular, our comparative statics results are useful when an increase in the lottery's riskiness increases the agent's optimal action, but an increase in the lottery's expected value decreases the agent's optimal action. For this kind of situation, we provide a tool to determine which of these two forces dominates -- riskiness or expected value. We apply our results in consumption-savings problems, self-protection problems, and in a Bayesian game.
In this paper we provide a novel family of stochastic orders, which we call the \alpha,[a,b] -concave stochastic orders, that generalizes second order stochastic dominance. These stochastic orders are generated by a novel set of "very" concave functions where \alpha parameterizes the degree of concavity. The \alpha,[a,b] -concave stochastic orders allow us to derive novel comparative statics results for important applications in economics that could not be derived using previous stochastic orders. In particular, our comparative statics results are useful when an increase in the lottery's riskiness increases the agent's optimal action, but an increase in the lottery's expected value decreases the agent's optimal action. For this kind of situation, we provide a tool to determine which of these two forces dominates -- riskiness or expected value. We apply our results in consumption-savings problems, self-protection problems, and in a Bayesian game.
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allow us to compare two lotteries, where one lottery has a higher expected value and is also riskier than the other lottery. The main motivation for introducing the
are generated by a novel set of "very" concave functions where \alpha parameterizes the degree of concavity. The
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-convex decreasing stochastic orders is that they
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