Reinsurance Cession Optimization

Status: BUILT & COMMITTED (D053 1L, 2026-06-29). The backing engine insmodel.L4.cession_optimizer (CessionOptimizer, @engine) is implemented on disk and committed: firmmodel/engines/cession_optimizer.py + tests/test_cession_optimizer.py (21 passing tests) + snap_M_055 + legacy_metadata/CessionOptimizer.yaml + validation_evidence/M-055/v1.0.0. What follows describes running, tested code (it composes four already-built, tested InsModel engines — no fabrication). The engine-existence flag (engine_registry status) is active; the model status stays under_development because 2L effective-challenge re-review owns the model state transition and the final pass thresholds (RAT-055 COND-055-01..05) per Decision 052.

Conceptual soundness (SR 11-7 / SR 26-2). M-055 is a DECISION / ORCHESTRATOR model — it introduces no new actuarial primitive. It composes four already-built, tested InsModel engines and runs a constrained 1-D grid search over the cession fraction c in [0,1]:

1. Genuine capital arbitrage. Ceding a block to an offshore affiliate (a) RELIEVES the US ceding entity's RBC via the NAIC Model-791 reinsurance credit — net_rbc = max(0, gross_rbc − reinsurance_credit), reinsurance_credit = ceded_reserve × credit_quality (taken directly from ReinsuranceEngine._compute_capital_relief / _compute_reinsurance_credit, INV-027-clamped); RBC relief is bounded (capped at gross_rbc; for credit_quality < 1 the haircut leaves relief < ceded reserve) — and simultaneously (b) LANDS the ceded reserve + supporting assets on the offshore balance sheet, where BSCREngine charges the BMA standard-formula modules. So consolidated required capital = net_RBC(c) + scalar × BSCR(c) is genuinely non-monotone: net_rbc(c) is non-increasing (floored at 0) and bscr(c) non-decreasing, so the sum is unimodal with an interior minimum where marginal relief is overtaken by marginal BSCR build. This is the documented central modelling challenge — reconciling NAIC RBC against BMA BSCR onto a common consolidated basis.
2. Cross-jurisdiction reconciliation on required-capital DOLLARS — the only coherent common basis. Both legs are statutory required-capital amounts (RBC total = ACL dollars; BSCR dollars). A documented A-283 consolidation-basis scalar (default 1.0) makes the FX / economic-basis alignment factor on the BSCR leg explicit and ratifiable rather than hidden. The optimizer does NOT convert RBC ratios into BSCR ratios.
3. AG-55 as a FEASIBILITY constraint, not an objective term — exactly its regulatory role. AG-55 gates whether a cession is adequate (unsecured shortfall fully asset-backed AND net worst-case surplus ≥ 0 across the 7 prescribed scenarios). The optimizer calls AG55Engine per candidate and EXCLUDES any candidate with ag55_passed == False. The optimum is the consolidated-capital-minimising cession among AG-55-feasible structures.
4. Composition, not reimplementation. By design, credit from ReinsuranceEngine; RBC relief from ReinsuranceEngine._compute_capital_relief (M-050 dollar base); BSCR from BSCREngine (M-054); AG-55 verdict from AG55Engine (M-005, ag55_results_v1.ag55_passed). (M-054's BSCREngine is now built and M-054 is active — so this composition runs against real, tested upstream engines, cross-checked to max abs err 0.00e+00.)

Algorithm. For each c on the grid (default linspace 0.0..1.0 step 0.05): (1) build candidate treaty with cession_pct = c, run ReinsuranceEngine → ceded_reserve(c), reinsurance_credit(c); (2) net_rbc(c) = max(0, gross_rbc − reinsurance_credit(c)); (3) BSCREngine on the assuming-entity balance sheet with best_estimate_liabilities = ceded_reserve(c) → bscr(c); (4) consolidated(c) = net_rbc(c) + scalar × bscr(c); (5) AG55Engine → feasible(c) = ag55_passed. SELECTION: optimal_cession_pct = argmin over feasible candidates of consolidated(c). If NO candidate is feasible, return c = 0 (no cession) honestly — never fabricate a passing structure. optimum_is_interior flags 0 < c* < 1. Pure deterministic search — no stochastic step, fully reproducible.

• Inputs (design): gross_book (gross_premium/benefit/reserve/rbc, n_periods), base_treaty (treaty_id, treaty_type, reinsurer_credit_quality, optional supporting_assets), offshore_balance_sheet (optional BSCR exposures other than the ceded reserve).
• Outputs (design): cession_optimization_v1 — summary (optimal_cession_pct, consolidated_required_capital, net_rbc_at_optimum, bscr_at_optimum, baseline_consolidated_capital, capital_saving, ag55_passed_at_optimum, optimal_treaty_id, optimal_treaty_type, n_feasible_candidates, n_candidates_evaluated, optimum_is_interior) + per-grid-point candidate frame.

• A-283 — Consolidation basis scalar (BSCR leg), default 1.0. The optimizer sums net NAIC RBC (M-050) + BMA BSCR (M-054) as required-capital DOLLARS onto a consolidated basis. This scalar makes the FX / economic-basis alignment factor on the BSCR (offshore) leg explicit and ratifiable rather than hidden. Default 1.0 = no adjustment. It is unvalidated against a disclosed consolidated group-capital figure (no live firm data, BV-032) and is the residual cross-jurisdiction reconciliation risk (RAT-055 COND-055-04) — a 2L effective-challenge item. Domain insmodel_offshore_capital.
• Cession grid (lower 0.0, upper 1.0, step 0.05) — a SEARCH control, not an economic assumption. The optimum is grid-resolution-accurate; the step is configurable.
• Which gross-book RBC drivers respond to cession. Net reserve/credit relief flows through the Model-791 credit; other RBC components are held at the gross dollar base unless declared (conservative — no extra relief claimed).
• Inherited via M-005 (AG-55 feasibility): A-001/A-002 (net liability cash flows) and A-090/A-091 (supporting-asset spreads/discounting). credit_quality and supporting-asset posture are treaty-declared inputs, not re-derived from counterparty financials (consistent with M-005).

These are honest current-state limitations of the built model — no fabricated bounds. (The residual gate is COND-055-04: the consolidated-basis A-283 sign-off + firm-data back-test — see Limitation 5 and the Validation Packet; the engine itself is built and tested per the top note and Methodology.)

1. Single decision variable. 1-D optimisation over a single cession fraction on one treaty/block; multi-treaty / multi-counterparty joint optimisation and treaty-type mix are out of scope.
2. Grid search, not a continuous solver. The optimum is grid-resolution-accurate (mitigated by the monotone-leg structure: one non-increasing + one non-decreasing leg → unimodal sum, so the grid argmin is reliable). Refine the step for precision.
3. Required-capital objective only. Cost of reinsurance (ceding commission, net cost) is NOT in the objective — a capital-efficient structure may be economically expensive. A capital-cost / economic-value objective is a future extension.
4. No cross-jurisdiction diversification credit. RBC and BSCR are summed as dollar required capital; no group diversification benefit is claimed across the two regimes (conservative). The A-283 consolidation-basis scalar (default 1.0) is itself unvalidated against a disclosed consolidated group-capital figure — the residual cross-jurisdiction reconciliation risk (RAT-055 COND-055-04, a 2L item).
5. Firm-data binding deferred (no live firm data, BV-032). DS-001 (FRED, inherited) feeds the AG-55 CFT/asset legs; DS-047 (NAIC AG-55 Form B) + disclosed BMA BSCR/ECR + RBC figures for a firm-specific cession-optimization opinion and an external reasonableness cross-check (PRU Prismic, APO Athene) are DEFERRED. Outputs illustrate the mechanics, not a firm filing — identical to the M-005 / M-054 posture. A Tier-1 §10.5 back-test data gap.
6. AG-55 feasibility inherits all M-005 limitations (NY-7 deterministic scenarios not a stochastic ESG, supporting-asset proxy fallback, treaty-declared credit_quality, static treaties / no recapture).
7. No-feasible-candidate degenerate path is handled honestly (returns no-cession, no fabrication).

2L re-review owns the state transition (Decision 052): the final pass thresholds, the consolidated-basis sign-off (RAT-055 COND-055-04), and the back-test data gap closure. The 1L build does not gate the state transition.

1L BUILD EVIDENCE PRESENT (D053, 2026-06-29). documentation_pack.validation_evidence is present: the pack is at modelling/validation_evidence/M-055/v1.0.0/ (README + worked_optimization_and_sensitivity.md). The engine is covered by tests/test_cession_optimizer.py (21 passing acceptance tests) and the registered deterministic snapshot snap_M_055. Every capital number is produced by the composed real engines on parameterized inputs — no firm capital figure is fabricated (BV-032).

1L acceptance tests (21, all passing): - consolidated = net_rbc + scalar × bscr, each leg equal to a direct component-engine call (composition, not reimplementation — net_rbc = ReinsuranceEngine._compute_capital_relief, bscr = BSCREngine, ag55_passed = AG55Engine). - net_rbc non-increasing and bscr non-decreasing in cession_pct (the monotone-leg structure that makes the sum unimodal). - Interior optimum when the RBC-relief vs BSCR-build tradeoff bites (0 < c* < 1, objective at optimum below both endpoints). - AG-55-infeasible candidates excluded from the argmin; no-feasible-candidate → no cession honestly. - Output-contract shape, consolidation-scalar application, governance metadata (M-055, ≥3 references), determinism.

Worked optimization (gold canonical inputs, scalar 1.0, grid step 0.05): the optimizer selects an interior optimum c* = 0.10 with consolidated required capital $4,320 (net_rbc $0 + bscr $4,320) versus a $40,000 no-cession baseline — a $35,680 saving — AG-55-feasible. The consolidated objective falls from $40,000 as the Model-791 RBC relief bites, bottoms at c = 0.10 (RBC fully relieved, offshore BSCR still small), then rises as BSCR overtakes the exhausted relief. Cross-check: each leg matches a direct component-engine call to max abs error 0.00e+00*. Full per-grid-point candidate frame + cession-% and A-283 sensitivities in the pack.

Required before this model can move to active status (2L acts — 1L does not self-ratify): - Conceptual-soundness review and independent effective challenge per MRM §10.2 (Tier-2), mrm-validator as independent challenger (RAT-055 COND-055-01..04). (M-054 must be active for the BSCR leg — landing via the post-RAT reconciler #3462; that is the downstream 2L governance gate, not the 1L build.) - Consolidated-basis sign-off — validation of the A-283 scalar against a disclosed consolidated group-capital figure once sourced (COND-055-04). - Firm-data back-test — close the DS-047 / disclosed BMA BSCR + RBC data gap (PRU Prismic, APO Athene).

Regulatory: - NAIC Actuarial Guideline 55 (AG LV) — Application of the Valuation Manual for Testing the Adequacy of Reserves Related to Certain Life Reinsurance Treaties. Affiliated/offshore reinsurance asset-adequacy testing (AAT); adopted Aug 13 2025, effective for the Dec 31 2025 Annual Statement, first AAT reports due to regulators by April 1 2026. The binding constraint on cession structuring. - BMA Bermuda Solvency Capital Requirement (BSCR) — Bermuda Monetary Authority statutory capital standard for the offshore assuming reinsurer. - NAIC Risk-Based Capital (RBC) — US statutory risk-based capital formula for the ceding entity. - Federal Reserve SR 26-2 (April 2026, supersedes SR 11-7) — Model risk management; applies to the platform via Decision 018 MRM Framework.

Internal: - Decision 018 (MRM Framework) — Management/decisions/018-mrm-framework-multi-regime.md; AG 55 / RBC / BSCR scope at insightalm/modelling/charters/mrm_framework.md §3.2. - Grounding study — vertical/research/03_insurance_gap_analysis.md, gap #2 (cross-firm 10-K analysis motivating the cession-optimization model).

Card change history. Code-side change history lives in git log of the component files.

• 2026-06-05 — stub created from registry data per Decision 023 Phase 5 / B-07.
• 2026-06-06 — 2L documentation review. Filled Methodology, Standards Coverage (new), Key Assumptions, Limitations, Validation Packet, References, and Dependencies narrative from the model/engine registry. Model was design-stage at the time: backing engine status: planned, no output contract, no assumptions, no validation evidence.
• 2026-06-07 — Paper-layer pass (Decision 053 Tranche C, citing #2310) — LATER FOUND HOLLOW. The registries, contract, assumption and this card were advanced to assert insmodel.L4.cession_optimizer (CessionOptimizer, @engine, v1.0.0) was implemented at firmmodel/engines/cession_optimizer.py with a 12-test suite, snap_M_055 snapshot and legacy_metadata/CessionOptimizer.yaml, and the engine status was flipped planned → active. The engine source was never committed — none of those artifacts exist on disk or in git (see the 2026-06-08 correction). The registered output contract cession_optimization_v1 and assumption A-283 (consolidation basis scalar, domain insmodel_offshore_capital) are the genuine paper deliverables, but bound to a non-existent producer/consumer.
• 2026-06-08 — 1L remediation of RAT-055-v1.0.2 (COND-055-05 + COND-055-01..04). Independent verification confirmed the 2L finding: firmmodel/engines/cession_optimizer.py, tests/test_cession_optimizer.py, snapshot snap_M_055, and legacy_metadata/CessionOptimizer.yaml are ALL absent on disk and in git (pytest collects 0 tests; snapshot script reports "no snapshot registered"; no commit ever added the engine). Reconciled the documentation layer to honest PLANNED / design-complete state (parallel to the M-054 bscr_engine correction): engine_registry status active → planned; contract_registry cession_optimization_v1 status active → planned (design-intent schema); assumption A-283 status active → planned (paper-bound until consumed); model_registry comments + documentation_pack reconciled; this card's Status/Methodology/Validation Packet/Key Assumptions rewritten from "BUILT" to "design intent / pending". The genuine engine build (COND-055-01) and the downstream contract-verification (02), assumption-consumption (03) and validation pack (04) remain honestly conditional pending the real engine — not fabricated. No outputs, tests, snapshots or validation numbers were invented.
• 2026-06-29 — REAL 1L BUILD (Decision 053, backlog §A / #2310). The engine is now genuinely built and committed: firmmodel/engines/cession_optimizer.py (the @engine CessionOptimizer with its ENGINE_CONTRACT — a constrained 1-D grid search composing ReinsuranceEngine + BSCREngine (M-054) + AG55Engine (M-005)), tests/test_cession_optimizer.py (21 passing acceptance tests), scripts/model_snapshots.py::snap_M_055 (registered deterministic snapshot), firmmodel/governance/legacy_metadata/CessionOptimizer.yaml (SR-11-7 archive), scripts/validate_cession_optimizer_sensitivity.py, and modelling/validation_evidence/M-055/v1.0.0 (worked optimization: interior optimum c* = 0.10, consolidated $4,320 vs $40,000 baseline; cession-% + A-283 sensitivities; composition cross-check max abs err 0.00e+00). Engine-existence flags flipped planned → active (engine_registry; contract_registry cession_optimization_v1; assumption A-283 now GENUINELY consumed and wired into M-055 inputs.assumptions). validation_evidence flipped missing → present (registry_deltas/M-055.yaml). The model status stays under_development and ratification_ref stays RAT-055-v1.0.2 — 1L does not self-ratify; the 2L effective-challenge re-review (RAT-055-v1.0.3) owns the model state transition, the consolidated-basis (A-283) sign-off and the firm-data back-test (COND-055-04). The 1L build clears the engine-build leg (COND-055-01) + COND-055-02 (contract emitted) + COND-055-03 (A-283 consumed). No firm capital numbers fabricated. (2L gate: RAT-055-v1.0.3 also requires M-054 active — landing via the post-RAT reconciler #3462.)
• 2026-06-29 — 1L LG-clearance pass (RAT-055-v1.0.3 low/non-gating findings, issue #3498). LG-055-06: the Components → Processing-engines (~L53), Output-contracts (~L56) and Standards-Coverage opening (~L69) sections still read "PLANNED / not yet implemented", contradicting the card's own BUILT header/Methodology/Change-Log — rewritten to the built state (CessionOptimizer engine, cession_optimization_v1 contract EMITTED, the A-283 consumption, the M-050/M-054/M-005 composition), kept honest about the conditionally-approved + firm-data-gated (COND-055-04) status. Card fingerprint re-stamped (model_doc_currency). LG-055-07: the engine-vs-model tier mismatch (engine_registry tier-1 vs model_registry/card tier 2) reconciled to Tier-1 — the §6.3 derivation (consolidated regulatory-capital output + composes/feeds Tier-1 capital models M-050/M-054/M-005; aligns with M-054's Tier-1 re-derivation and the engine_registry tier-1) is now documented in the Materiality justification; model_registry tier: 2 → 1 set via registry_deltas/M-055.yaml. The latent §6.3 trigger-(b) sr_26_2-as-Tier-1 vs §6.5 scope-tag-in-practice wording gap is a framework-owner / 2L call — flagged in #3498, NOT self-resolved here. 1L does not self-ratify; the tier reconciliation is a defensible 1L call surfaced for 2L confirmation in RAT-055-v1.0.3. No code, no fabricated figures.