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

精算论坛第295期讲座

(2026年10月27日)

讲座主题一：SpectralVolterraprocesses and the fractional volatility puzzle

摘要：Stochastic volatility models driven by a fractional Brownian motion cannot account for bothroughnessof volatility paths and long memory, a problem known in the literature as the fractional volatility puzzle. This puzzle is a consequence of the self-similarity property of the fractional Brownian motion, which connects its fractal dimension D and its Hurst exponent H by the celebrated formula D=2-H.Fortunately, there exist alternative Gaussian processes which do not obey the self-similarity property,allowing for both rough paths and long memory of volatility by calibrating D and H separately. One such process is the so-called Generalized Cauchy process, whose covariance follows a two-parameter inverse power function. In the past, the idea to use a Generalized Cauchy process as a stochastic volatility model for option pricing has been hampered by the lack of any simple stochastic integral representation of this process.In this research, we establish an explicit stochastic integral representation of theGeneralized Cauchy process, using known results about the spectral density of its covariance kernel. We then adapt this spectral representation toconstruct an explicit GaussianVolterraprocess, which we call SpectralVolterraprocess, whose stationary distribution coincides with the Generalized Cauchy process. Since option pricing expansion formulas are available for GaussianVolterravolatility models, the spectralVolterraformulation offers a possible approach to overcome the fractional volatility puzzle in practice.

报告人：

Dr.NicolasLangrenéis an Associate Professor in the Department of Financial Mathematics of Beijing Normal-Hong Kong Baptist University. Prior to this, he was Research Scientist at the CSIRO in Australia, from 2014 to 2022, workingon multidisciplinary academic and industrial research projects for the industry and the Australian government. He holds a PhD in applied mathematics from theUniversitéParisCité, France. His multidisciplinary research interests include quantitative andcomputational finance, stochastic control and stochastic optimization, machine learning and kernel methods, computational statistics and data visualization. He published in top journals of different disciplines, including Mathematical Finance, Annals of Applied Probability, Journal of Computational and Graphical Statistics, SIAM Journal on Numerical Analysis, and Resources Policy. His current research focuses on computational kernel methods and their application in quantitative finance.

讲座主题二：Model-free option hedging using deep Hedged Monte Carlo with application to variable annuities

摘要：The accurate pricing and hedging of variable annuities is known to be difficult both from the methodological and computational fronts, as it involves the joint mathematical modelling of multiplestochastic factors including equity risk, interest rate risk, longevity risk, as well as humanbehaviourand preferences. Another, often overlooked, difficulty with variable annuity pricing and hedging is model risk. Indeed, such retirement products are expected to be effectual for very long time horizons, potentially decades. It is obviously a great challenge to develop a multivariatestochastic model for all the aforementioned stochastic factors that remains reliable and robust over such long time periods.

When it comes to solving such high-dimensional stochastic control problems, the most successful methods are based on Monte Carlo simulations. The conventional way to generate sample paths is to simulate from a fixed, prescribed model for the stochasticfactors. An alternative sampling approach, which is more robust to model risk, is bootstrap resampling from historical time series. While this data-driven approach has previously been used successfully for long-term optimal pension portfolio problems, it has not yet been used in the context of option pricing. The key reason for this is that the classical price options framework requires a change of measure for thehedgeablestochastic factors, and then simulates them under the resulting risk-neutral measure, in which hedging is implicitly applied. Thus, the use of historical block bootstrapping for the pricing of variable annuities would therefore requireto bypass this change of measure and keepworking directly with historical measures.

The Hedged Monte Carlo technique allows precisely this, by explicitly estimating and simulating the hedging strategy during each time period of the discrete hedging strategy of the financial product under consideration. In this talk, we revisit the Hedged Monte Carlo methodology, and extend it in three ways. First, we suggestto estimatethe discrete hedging strategy using artificial neural networks to improve the applicability of the method to high-dimensional hedging problems, such as those encountered in variable annuities. Second, we sample the historical stochastic factors using block-bootstrapping, to make the method more robust to long-term model risk. Finally, we apply this proposed model-free deep hedged Monte Carlo methodology to the pricing and hedging variable annuities. Our numerical experiments validate the accuracy of the method, and its effectiveness to deal with long-term variable annuity contracts with multiple sources of uncertainties.

报告人：

Dr. Wen (Monica) Chen is an Assistant Professor in the Departmentof Artificial Intelligence at Beijing NormalHong Kong Baptist University(BNBU). Sheobtained her PhD in Computational and Financial Mathematics from the University of Western Australia, her M.Sc. in Computational Mathematics from Wuhan University, and her B.Sc. in Mathematics and Applied Mathematics from Beijing Institute of Technology.

Beforejoining academia, she spent 20142022 at Australia’s CommonwealthScientific and Industrial ResearchOrganisation(CSIRO), firstas a Postdoctoral Fellow andthenas a Research Scientistbased inSydney and Melbourne. She contributed to multiple government strategic initiatives and industrycommercial projects spanning asset management, retirement planning, natural resourcemanagementand bushfiredata analytics.Her researchinterestinclude quantitative finance, actuarial science and deep learning to address highdimensional stochastic control problems in derivative pricing, retirement management and climate policy decision-making.

讲座时间：2026年10月27日（周二）

下午14:00-16:00

报告地点：沙河校区13号楼209教室

邀请人：韦晓