More on Adaptive Risk Engine

1 | Mission & Hard Targets

Helios uses a convex optimization model solved every Bitcoin block. The solver chooses a maximum loan-to-value (LTV*) and liquidation bonus (LP*) that satisfy one non-negotiable safety bar:

Probability(collateral after worst-case delay < (1 + LP*) × debt) ≤ 0.1 %

This 99.9 % solvency guarantee keeps expected bad debt near zero. Capital efficiency is then maximized up to that risk ceiling by pushing LTV as high as the constraints allow.

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2 | Data Feeds & Model Inputs

Symbol	Feed (every block)	Why it matters
σ	1-hour and 24-hour realized BTC volatility	Determines worst-case price drop window
M	Median sat/vB required for next-block confirmation	Approximates liquidation-delay risk
LiqDepth	Rolling 24-hour spot-market volume	Caps collateral that can be safely sold

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3 | Optimization Blueprint

Minimize   ExpectedBadDebt(LTV, LP ; σ, M) – λ · LTV
Subject to convex safety, liquidity, and user-experience constraints

• Convexity guarantees a unique, globally optimal solution that anyone can verify.

• The solver runs off-chain for speed; the resulting parameters are written directly to contract state and take effect in the next block—no multisig or admin key required.

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4 | Block-to-Block Guardrail

Parameter drift is rate-limited to no more than 2 percentage points of LTV per block in normal conditions, giving borrowers time to react without whiplash.

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5 | Illustrative Parameter Map

Market Regime	σ (24 h)	M (sat/vB)	Max LTV*	LP*	Borrow APR†	Supply APY†
Calm	< 40 %	< 5	80 %	5 %	5 %	3 %
Elevated	40–80 %	5–25	65 %	8 %	9 %	6 %
Stressed	80–120 %	25–80	50 %	12 %	14 %	9 %
Crisis	> 120 %	> 80	40 %	15 %	18 %	12 %

†Assumes 75 % pool utilization and Helios’s kinked interest curve.

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6 | Scenario Simulation for Stakeholders

Regulators, auditors, and investors can replay historical data or craft what-if shocks against the open-source solver to see how Helios would respond:

Scenario	Inputs Fed to Model	Engine Response	Outcome
Black-Thursday-style crash	σ peaks at 150 %, M hits 120 sat/vB	LTV drops to 40 %, LP jumps to 15 % within two blocks	No under-collateralization
Exchange flash crash	–12 % price in 30 min, normal M	LTV throttles from 80 % to 60 %	Loans stay solvent; partial liquidations only
Sudden mempool spike	σ steady, M increases 10× for 3 hours	LP increases 300 bps, LTV trims 5 pp	Liquidators remain profitable despite higher fees

Because the model and inputs are transparent, third parties can validate every decision path and confirm that the 0.1 % insolvency ceiling is upheld under each stress run.

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7 | More on Why It Matters

• No black boxes – Linear and convex math—not opaque AI—drives every change.

• Real-time enforcement – Parameters shift block by block, not via slow governance votes, preventing the lag that hurt earlier protocols.

• Plug-and-play audits – The solver and its test harness are open source; regulators can run them locally to replicate any decision curve.

Helios’s risk engine delivers bank-grade transparency with blockchain-level speed, giving lenders, borrowers, and oversight bodies a shared, deterministic view of protocol safety.