AI 410 · Year 4 · Semester 1 · 3 credits · AI & Machine Learning

Decision Under Uncertainty & Reinforcement Learning

From static risk aversion to sequential intelligence: mastering dynamic control, reinforcement learning, and optimal actuarial decision-making.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

The Dynamic Horizon: Reinforcement Learning in the Solvency Era

When climate volatility and fierce rate competition threaten NorthStar Mutual with a ratings downgrade, newly appointed Lead AI Actuary Maya Lin must replace rigid static spreadsheets with safe, mathematically rigorous reinforcement learning models before the annual solvency audit.

Protagonist · Maya Lin, FSA, CERA, Lead AI Actuary at NorthStar Mutual

Setting · NorthStar Mutual Headquarters in Chicago, navigating state insurance regulatory audits, board oversight, and volatile Midwest convective storm seasons

Stakes · A multi-notch AM Best downgrade to B-plus, regulatory takeover under risk-based capital impairment, and seventy million dollars in unhedged catastrophe losses if the insurer's dynamic pricing and reinsurance policies fail.

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Episodes

Season finale: Maya deploys a distributionally robust, Solvency II-compliant safe reinforcement learning framework to dynamically optimize multi-peril catastrophe reinsurance purchasing, reducing five-year ruin probability below one-tenth of one percent while satisfying actuarial governance standards.

From the lecturer: Welcome to AI 410. In your earlier courses, you evaluated static risk: computing a net premium, calculating a single reserve, or estimating a distribution parameter from historical claim data. In the real world, actuarial decisions are dynamic, feedback-driven, and sequential. How much surplus do you retain each quarter when market rates change? How do you price insurance renewals when competitor actions alter policyholder lapse behaviour? How do you dynamically hedge a variable annuity guarantee under stochastic volatility?\n\nTo master this material, keep a dual workstation: engineering grid paper on your left for state-transition diagrams and Bellman derivations, and a clean Python notebook on your right for dynamic programming algorithms. Trace every finite-state MDP by hand before writing your backward induction loops. While AI 410 does not map to a single preliminary exam, it bridges the gap between classical risk theory and modern computational finance, preparing you directly for advanced research, quantitative underwriting, and predictive AI deployments. Dive in, derive every optimality operator, and let us build decision policies that remain robust even when the environment fights back.

Cold open

At 6:15 AM on a Monday, Maya stares at a spreadsheet projection showing NorthStar Mutual's commercial property book. The static expected monetary value model recommends accepting a six-hundred-million-dollar coastal portfolio for a modest three-million-dollar premium margin, completely ignoring that a single Category Four storm would wipe out thirty-five percent of statutory surplus in one afternoon.

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Transcript

State the von Neumann–Morgenstern axioms and explain how expected utility resolves the St. Petersburg paradox
Derive the Arrow–Pratt measures of absolute and relative risk aversion (ARA and RRA) and link them to the risk premium via Taylor approximation
Calculate certainty equivalents and maximum willingness-to-pay for insurance under CARA and CRRA utility functions
Connect static utility theory to risk-sensitive objective functions in reinforcement learning