Frontiers of Statistical Research on Actuarial Science and Risk Management

Abstract: In 2015, Jianxi Su and his co-authors introduced the notion of paths of maximal dependence, which truthfully assess the extent at which dependent risks, such as financial instruments, interact with each other. Although the paths are often clearly visible in simulated data, they are nevertheless quite difficult to empirically estimate.  In 2021, Takaaki Koike and his co-authors succeeded, among many other things, to develop statistical inference for tangent lines of the paths of maximal dependence. Around the same time, Ning Sun and her co-authors found a way to construct empirical estimators for the paths and thus for the indices of maximal dependence. In this talk, I will discuss these research contributions to the area of measuring (tail) dependence.

Nariankadu Shyamalkumar

Abstract: The tail dependence coefficient is a popular bivariate tail dependence measure. Akin to the correlation matrix, a multivariate tail dependence measure is the tail dependence matrix (TDM) constructed using these bivariate measures. The problem of determining whether a given d × d matrix is a TDM, the realization problem, is significantly more complex than determining it is a correlation matrix. Using an LP formulation, we show that the combinatorial structure of the constraints is related to the intractable max-cut problem in a weighted graph. This connection provides an avenue for constructing parametric classes admitting a polynomial in d algorithm for determining membership in its constraint polytope. We show how the inherent symmetry and sparsity in the parametrization of a class of TDMs help significantly simplify the LP formulation, leading to polynomial complexity of its constrained realization problem - with some O(1) in complexity. We also study the subset of TDMs supported by the t-copula family. This is joint work with Siyang Tao (Ball State University).

Abstract: Recently, tail risk measures such as Haezendonck–Goovaerts (H-G) and Gini-Functional risk measures have been popular in actuarial science and applied widely in insurance and optimal asset allocation. In this talk, we first consider the extreme risk measures that evaluate the impact of the portfolio from the systematic under extreme scenarios. Next, we discuss the expression for computing the sensitivity of tail risk measures and propose the nonparametric estimator and explore its asymptotic behavior.  Furthermore, we reveal the sensitivity analysis toward tail risks and illustrated them in real data analysis.

Abstract: As an important tool in financial risk management, stress testing aims to evaluate the stability of a financial system under some potential large shocks from extreme yet plausible scenarios of risk factors. The effectiveness of a stress test crucially depends on the choice of stress scenarios. In this paper we consider a pragmatic approach of stress scenario estimation that aims to address several practical challenges in the context of real life financial portfolios of currencies from a bank. Our method utilizes a flexible multivariate modelling framework based on vine copulas.