The 4^th Academic Luncheon of the Digital Technology and Finance

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.

Speaker Introduction:
Xin Li, is a lecturer at the School of Finance, Zhongnan University of Economics and Law. He graduated from the School of Mathematics and Statistics, Huazhong University of Science and Technology, majoring in Statistics, and visited UNSW Business School from 2018 to 2019. In March 2021, he joined Zhongnan University of Economics and Law as a teacher of the School of Finance. His research mainly focuses on Actuarial, the application of stochastic analysis and stochastic control in insurance actuarial. His current results have been published in the international actuarial journal Insurance: Mathematics and Economics and the domestic journal Journal of Applied Mathematics.