Robust risk evaluation of joint life insurance under dependence uncertainty

Battle Count: 84

The paper is primarily focused on actuarial science and insurance risk evaluation rather than quantitative trading. However, the use of copula models, VaR, Expected Shortfall, and dependence uncertainty quantification are broadly relevant to quantitative finance. The linear programming approach for computing risk bounds under model uncertainty could inform risk management practices in trading desks dealing with multi-asset or multi-counterparty exposures. The concordance order and Fréchet-Hoeffding bounds are also used in multi-asset option pricing. Overall, the direct applicability to trading strategies is limited.

The theoretical framework requires understanding of copula theory, distortion risk measures, concordance order, and mathematical programming. The computational implementation involves setting up and solving combinations of linear programs (up to m-bar + 1 LPs for ES bounds), which is tractable with standard LP solvers. The main complexity lies in: (1) identifying the representation (2) for a given contract, (2) constructing the linear constraints (C10)-(C12), (3) handling the piecewise structure of VaR and ES distortion functions, and (4) choosing appropriate uncertainty levels epsilon. The paper provides explicit LP formulations in Appendix C, reducing implementation ambiguity.

R scripts to reproduce all numerical results are stated as available upon request from the author. The paper provides detailed mathematical formulations, explicit linear program descriptions in Appendix C, and parameter settings (Gompertz law parameters, Gumbel copula delta=1.96, loading lambda=0.06, confidence levels alpha_VaR=0.99 and alpha_ES=0.975). However, no public repository is linked, and the scripts require contacting the author. The theoretical proofs are fully provided in Appendix B.