Department of Mathematics

Abstract: Underreporting losses is a prevalent behavior in insurance that is well supported by the empirical study. The goal of this talk is, however, to propose a theoretical model to explain such a behavior. To achieve this, we take an optimization perspective and consider an optimal control problem in which the insured decides whether she should report a (covered) loss. This talk will be based on the following two papers:

1. Jingyi Cao, Dongchen Li, Virginia R. Young, and Bin Zou (2023). Equilibrium reporting strategy: Two rate classes and full insurance. Journal of Risk and Insurance, https://onlinelibrary.wiley.com/doi/10.1111/jori.12451.
2. Jingyi Cao, Dongchen Li, Virginia R. Young, and Bin Zou (2024). Strategic underreporting and optimal deductible insurance. ASTIN Bulletin, https://www.researchgate.net/publication/379300509_Strategic_Underreporting_and_Optimal_Deductible_Insurance. 

This is a joint event with the UConn Control and Optimization Seminar.

Abstract. We propose efficient and reliable simulation schemes for pricing options under the stochastic-alpha-beta-rho (SABR) model. The standard two-step simulation procedures involve (i) simulation of the integrated variance conditional on terminal variance and (ii) simulation of the terminal forward price conditional on terminal variance and integrated variance. Most simulation schemes rely on the Islah approximation formula of the conditional distribution of the terminal asset price, which is seen to fail the martingale condition in general. We embed three enhanced features in our proposed simulation schemes. Firstly, we approximate the terminal forward price as the constant elasticity of variance (CEV) process that satisfies the martingale condition, an important property that precludes arbitrage. Secondly, we adopt the displaced Poisson-mixture Gamma distribution for the exact simulation of the underlying CEV process in the simulation of the terminal forward price conditional on integrated variance and terminal variance. Thirdly, we use the shifted lognormal approximation of the integrated variance to compute the integrated variance. Our enhanced procedures avoid the tedious Laplace inversion algorithm in integrated variance calculations and non-efficient inverse transform in the forward price calculations in earlier simulation schemes. Numerical results demonstrate our simulation schemes to be highly efficient, accurate, and reliable.

Speaker’s short bio: Dr. Choi is an associate professor with tenure at Peking University HSBC Business School in Shenzhen, China. He obtained his PhD in applied mathematics from Massachusetts Institute of Technology in 2005 and BS in mathematics from the Korean Advanced Institute of Science Technology in 2000. After his PhD, he worked in the industry as a quant for several years in BNP Paribas and Goldman Sachs. His research interests include quantitative finance, mathematical modeling, numerical methods, and data science. Please visit his website https://english.phbs.pku.edu.cn/2016/fulltime_0826/81.html for more information.

Speaker: Gordon Slade (UBC)

In theory, proof assistants are a useful tool for validating mathematical claims. We will use simplicial topology as a case study to look at what goes into formalizing mathematics from pen and paper to the digital world. This is based on previous work with Stefan Friedl focused on formalizing stellar subdivisions of simplicial complexes. I will present a few anecdotal stories from our project that demonstrate some of the challenges involved. Topics include (but are not limited to) what changes when we introduce types to topology, decidability and computational complexity concerns, and what to do when the proof is left as an exercise for the reader.

Join us in the Logic Colloquium for Xinhe Wu (NCSU)!

Details t.b.a.

All welcome!