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

Battle Count: 77

The paper is primarily focused on insurance risk management and regulatory capital allocation rather than trading strategies. However, the CoHM risk measure and its asymptotic properties are relevant to tail risk management in portfolios, systemic risk assessment in financial markets, and capital allocation decisions. The FGM dependence structure and extreme value theory tools could inform risk models used in quantitative trading, particularly for tail risk hedging and portfolio stress testing. The connection to CoVaR/CoES frameworks makes it relevant for systemic risk monitoring in financial markets.

The theoretical derivations involve advanced extreme value theory, second-order regular variation, and copula modeling. Implementing the second-order asymptotic formulas requires careful handling of auxiliary functions, tail indices, and dependence parameters. The numerical optimization of the CoHM objective function (infimum over x) requires one-dimensional optimization. Empirical applications require marginal distribution fitting, probability integral transformation, and FGM parameter estimation via MLE. The formulas are explicit but involve complex expressions with Gamma and Beta functions, second-order parameters, and multiple dependence terms.

The paper provides detailed mathematical derivations, explicit formulas for all three MDA cases, and specifies parameter settings for numerical examples. R code functions (optimize) are mentioned for computation. However, no GitHub repository or code is explicitly provided. The empirical datasets (dataCar from insuranceData package, danishmulti from CASdatasets) are publicly available in R packages. Full proofs are provided in the appendix.