Abstract：

We study the Neyman-Pearson theory for convex expectations or equivalent convex risk measures on L^{∞}(μ). Without assuming that the level sets of penalty functions are weakly compact, a fixed representative pair (P^{∗},Q^{∗}) is found by a new method different from the convex duality method. Then we show that the optimal tests are just the classical Neyman-Pearson tests between the representative probabilities P^{∗} and Q^{∗}. Finally, we apply our results to a shortfall risk minimizing problem in an incomplete financial market.  （With Chuanfeng Sun）.

Biography:

嵇少林，现为山东大学金融研究院教授、博士生导师，师从彭实戈院士。1999年至今在山东大学工作。研究领域为金融数学、金融经济学、随机优化和非线性期望理论。近年来，嵇少林在《Review of financial studies》, 《Operations research》,《Probability theory and the related fields》和《SIAM Control and Optimization》等杂志上发表了一系列的成果。对金融市场中的学习理论、资本资产定价、随机优化问题和非线性期望理论进行了系统的研究。

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