Abstract:

In traditional research in insurance and finance, the study of occupation times are all discussed when the red zone is either one-sided or two-sided interval. In this paper, we study generalized occupation times in a special red zone which can be linked to liquidation time under a two-barrier two-state liquidation framework which is a simplification of liquidation framework of Li et al. (2020) by ignoring the liquidation barrier, we express the Laplace transform of generalized occupation times in terms of scale functions under the spectrally negative Levy process, and present that the density of the generalized occupation time satisfies a convolution integral equation. Based on the generalized occupation time introduced, we further introduce a new kind of option referred to as two-barrier proportional step options which are variants of the conventional proportional step options, and then derive the Laplace transform of the price of this kind of options. Some numerical studies are presented.

主讲人介绍：

李鑫，中南财经政法大学金融学院讲师。毕业于华中科技大学数学与统计学院统计学专业。2018年-2019年访问新南威尔士大学商学院。2021年3月入职中南财经政法大学担任金融学院教师。研究主要关注于：保险精算，随机分析和随机控制在保险精算中的应用。目前成果发表和接收于国际精算杂志Insurance: Mathematics and Economics和国内期刊《应用数学学报》。