随机度量理论及其应用

本项目利用随机度量理论与随机凸分析为工具研究动态风险度量理论，提出新的模型空间并进一步研究动态风险度量的表示与时间一致性问题。对随机赋范模与随机局部凸模发展一种新的紧性理论，企图将经典泛函中的KKM映射理论与Tychonoff不动点定理推广到随机局部凸模上，并进一步探索它们在不完备市场中的均衡定价理论中的应用。

The project makes use of random metric theory and random convex analysis to study dynamic risk measures,proposing the new model spaces for dynamic risk measures and further studying their representation and time-consistency problems. Besides, we hope to develop a new theory of compactness for random normed modules and random locally convex modules in order to generalize the famous KKM theorem and Tychonoff fixed point theorem to random locally convex modules, further investigating their applications to equilibrium pricing in incomplete markets.