广义Choquet积分的Jensen不等式及其在风险规避中的应用
On Jensen's inequality for generalized Choquet integral with an application to risk aversion
摘要：
本文给出了广义Choquet积分关于容度对的Jensen不等式成立的充要条件。接下来，我们将所得结果应用到风险厌恶理论中，通过提供效用函数和能力的假设，使代理人厌恶风险。此外，我们还证明了Arrow-Pratt定理可以推广到用广义Choquet积分代替期望的情形。
英文摘要：
In the paper we give necessary and sufficient conditions for the Jensen inequality to hold for the generalized Choquet integral with respect to a pair of capacities. Next, we apply obtained result to the theory of risk aversion by providing the assumptions on utility function and capacities under which an agent is risk averse. Moreover, we show that the Arrow-Pratt theorem can be generalized to cover the case, where the expectation is replaced by the generalized Choquet integral.
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