arXiv subjects

Bingzhen Geng

Publications and source records attributed to Bingzhen Geng.

4 recordsLinked to original sources

arXiv2026

The conditional higher moment risk measure: second-order asymptotics with FGM contagion

This paper investigates second-order asymptotic expansions for the conditional higher moment (CoHM) coherent risk measure under a Farlie-Gumbel-Morgenstern (FGM) dependence structure, capturing a weak contagion between a primary loss risk and a reference risk. Assuming that the primary risk belongs to the Fr\'echet, Weibull, or Gumbel maximum domain of attraction, we systematically derive second-order asymptotic expansions using extreme value theory and second-order regular variation theory. Compared with existing first-order results, our refined approximations capture higher-order tail behavior and dependence effects more accurately. Numerical simulations confirm that the second-order asymptotics substantially reduce approximation errors, especially at extreme confidence levels. Empirical applications to insurance claim data further illustrate the practical superiority of the second-order approach.

q-fin.RM↗

arXiv2025

Second-order Asymptotic Analysis of Tail Probabilities of Bidimensional Randomly Weighted Sums

Motivated by a bidimensional discrete-time risk model in insurance, we study second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are essentially modeled as randomly weighted sums $S_n^{\xi}=\sum_{i=1}^n\xi_iX_i$ and $T_m^\eta=\sum_{j=1}^m\eta_{j}Y_{j}$ for any fixed $n,m\in\N$, in which it is assumed that the primary random variables $\left\{$X,Y$,$X_i,Y_i$:i\in \N\right\}$ form a sequence of real-valued, independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution and the random weights $\left\{\xi_i,\eta_i:i\in \N\right\}$ are bounded, nonnegative and arbitrarily dependent, but independent of the primary random variables. Under the assumption that two marginal distributions of the primary random variables are second-order subexponential, we first obtain the second-order asymptotic formulas for the joint and sum tail probabilities, which generalize and strengthen some known ones in the literature. Furthermore, by directly applying the obtained results to the above bidimensional risk model, we establish second-order asymptotic formulas for the corresponding tail probabilities. Compared with the first-order ones, our numerical simulation shows that the second-order asymptotics are much more precise.

math.PR↗

arXiv2024

Asymptotics of Systemic Risk in a Renewal Model with Multiple Business Lines and Heterogeneous Claims

Systemic risk is receiving increasing attention in the insurance industry. In this paper, we propose a multi-dimensional L\'{e}vy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a business line of an insurer. We use the systemic expected shortfall (SES) and marginal expected shortfall (MES) defined with a Value-at-Risk (VaR) target level as the measurement of systemic risk. Assuming that all the claim sizes are pairwise asymptotically independent (PAI), we derive asymptotic formulas for the tail probabilities of discounted aggregate claims and the total loss, which hold uniformly for all time horizons. We further obtain the asymptotics of the above systemic risk measures. The main technical issues involve the treatment of uniform convergence in the dynamic time setting. Finally, we perform a detailed Monte Carlo study to validate our asymptotics and analyze the impact and sensitivity of key parameters in the asymptotic expressions both analytically and numerically.

q-fin.RM↗

arXiv2024

Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification

Systemic risk measures play a crucial role in analyzing individual losses conditional on extreme system-wide disasters. In this paper, we provide a unified asymptotic treatment for systemic risk measures. First, we classify them into two families of Value-at-Risk- (VaR-) and expectile-based systemic risk measures. While VaR-based risk measures have been extensively studied, in the latter family, we propose two new systemic risk measures named the Individual Conditional Expectile (ICE) and the Systemic Individual Conditional Expectile (SICE), as alternatives to Marginal Expected Shortfall (MES) and Systemic Expected Shortfall (SES). Second, to characterize general mutually dependent and heavy-tailed risks, we consider a multivariate loss system following a multivariate Sarmanov distribution with common marginal distributions exhibiting second-order regular variation. Third, within this setting, we provide second-order asymptotic results for both families of systemic risk measures. These results extend standard first-order asymptotics and allow for more accurate tail approximations. Through numerical and analytical examples, we demonstrate the superiority of second-order asymptotics in accurately assessing systemic risk. We further conduct a comprehensive comparison between expectile-based and VaR-based systemic risk measures. The results indicate that expectile-based measures often yield higher asymptotic accuracy than VaR-based ones, emphasizing the former's potential advantages in reporting extreme events and tail risk. As a financial application, we use the asymptotic treatment to discuss the diversification benefits associated with various risk measures. Finally, we extend and obtain the second-order asymptotic formulas for generalized-quantile-based systemic risk measures with power functions.

q-fin.RM↗