教育部人文社科重点研究基地中央财经大学中国精算研究院学术活动
精算论坛讲座第213期
(2022年11月23日)
讲座主题一：Frame projection method for pricing barrier options under Lévy processes
摘要：The talk deals with “the frame projection method” (PROJ-method) for pricing discretely monitored barrier options for a wide class of Lévy.The method uses a backward induction approach and the fast Fourier Transform algorithm for efficient computing the convolution with the probability density. The key idea behind the approach involves approximating the log-return density by its orthogonal projection onto a space of compactly supported basis elements. A discrete convolution of the projected density with a set of value coefficients at each time step is represented as a Toeplitz matrix-vector multiplication, which can be efficiently implemented by means of the fast Fourier transform.
报告人：Oleg Kudryavtsev
He is Head of the Department of Computer Science and Customs Technologies at the Rostov Branch of Russian Customs Academy and Professor at the Institute of Mathematics, Mechanics and Computer Science of Southern Federal University. He is an expert in Computational Finance and Applied Mathematics, a member of the international research group MathRisk. Oleg Kudryavtsev holds a Degree of Doctor of Science in Physics and Mathematics (Russian analog of Habilitation Degree) from Central Economics and Mathematics Institute of Russian Academy of Science, (Moscow, Russia). The field of his research interests includes the development of fast and efficient computational algorithms for pricing path-dependent options and risk estimation in models admitting jumps (numerical Wiener-Hopf factorization, Monte Carlo methods, finite difference schemes, integral transform methods). He has published in the international journals: Quantitative Finance, Journal of Computational Finance, Finance & Stochastics, International Journal of Theoretical & Applied Finance etc.
讲座主题二：A Fourier-cosine Method for Finite-time Ruin Probabilities
摘要：In this paper, we study the finite-time ruin probability in the risk model driven by a Levy subordinator, by incorporating the popular Fourier-cosine method. Our interest is to propose a general approximation for any specified precision provided that the characteristic function of the Levy Process is known. To achieve this, we derive an explicit integral expression for the finite-time ruin probability, which is expressed in terms of the density function and the survival function of Lt. Moreover, we apply the rearrangement inequality to further improve our approximations. In addition, with only mild and practically relevant assumptions, we prove that the approximation error can be made arbitrarily small (actually an algebraic convergence rate up to 3, which is the fastest possible approximant known upon all in the literature), and has a linear computation complexity in a number of terms of the Fourier-cosine expansion. The effectiveness of our results is demonstrated in various numerical studies; through these examples, the supreme power of the Fourier-cosine method is once demonstrated.
报告人：刘芳达博士
刘芳达博士2015年毕业于加拿大滑铁卢大学并获得精算学博士学位，现任该校统计与精算系助理教授。她的研究方向侧重于最优保险/再保险设计、保险问题中的模型不确定性、风险度量以及风险分担。她的研究成果发表于国际四大精算期刊的Insurance：Mathematics & Economics，Astin Bulletin等。
讲座时间：2022年11月23日 下午19:00-21:00
报告地点：腾讯会议（会议ID：284 249 610）
邀请人：韦晓
