ACT 410 · Year 4 · Semester 1 · 3 credits · Actuarial

Enterprise Risk Management, Risk Measures & Capital

From axiomatic risk measures to enterprise balance sheets: the mathematical architecture of capital, dependence, and solvency.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

The Solvency Frontier

When a mid-sized composite insurer faces a sudden credit rating downgrade and regulatory intervention, newly appointed Chief Risk Officer Maya Lin must overhaul the firm's enterprise risk architecture from the ground up before the annual board solvency audit.

Protagonist · Maya Lin, FSA, CERA, newly promoted Chief Risk Officer at Beacon General & Life Assurance.

Setting · Beacon Assurance Headquarters in Hamilton, Bermuda, with operating subsidiaries across the United States and Europe.

Stakes · Beacon faces a four hundred and twenty million dollar solvency deficit, imminent regulatory sanctions from both the NAIC and European supervisors, and a catastrophic rating downgrade by AM Best that would freeze its commercial lines.

Pick an episode

Episodes

Season finale: Maya delivers a unified, mathematically rigorous Own Risk and Solvency Assessment to the board and regulators, replacing flawed linear models with copula-driven tail risk allocations and reverse stress tests that safeguard the firm's capital.

From the lecturer: Welcome to ACT 410. In this capstone actuarial risk course, we transition from standalone loss modeling to enterprise-level solvency, capital allocation, and risk governance. To master this material, keep a dual-track workspace: a dedicated derivation notebook for pencil-and-paper proofs of coherence, distortion operators, and Euler marginal allocations, alongside a Python or R environment for simulating non-linear copulas and extreme value quantiles. This course directly targets the syllabus requirements for the CERA credential, the SOA ERM Specialty Exam, and CAS Exams 7 and 9. When viewing each lecture, pause before every mathematical reveal to test whether you can predict why a metric fails subadditivity or how diversification breaks down under asymmetric tail dependence. Pay strict attention to the interplay between regulatory constraints (Solvency II and NAIC RBC) and internal economic capital models. ERM is not merely compliance; it is the quantitative science of strategic survival under extreme uncertainty. Approach every formula with the skepticism of a chief risk officer: question the tail assumptions, isolate the dependence structure, and verify the capital stability.

Cold open

At six forty-five on a rainy Monday morning, Maya Lin steps into Beacon's executive boardroom to find the Chief Actuary staring at a terminal screen. The preliminary regulatory capital filing shows that merging their commercial property and cyber liability units causes the combined required capital to spike by seventy million dollars more than the sum of their standalone requirements.

preparing lecture…

Transcript

State and interpret the four Artzner et al. (1999) axioms of coherent risk measures in the context of solvency capital.
Prove why subadditivity is mathematically indispensable for penalising concentration and rewarding diversification.
Distinguish between coherent and convex risk measures and explain when positive homogeneity fails in illiquid markets.
Demonstrate analytically and numerically how Value-at-Risk (VaR) violates subadditivity for heavy-tailed or non-normal credit portfolios.