/* InverseDesign.jsx — the methodology demo Sliders = target outcome (premium reduction, capital efficiency, tail tolerance, regulatory headroom) Output = a recommended "boundary configuration" — coverage stack with constitutional scoring */ const COVERAGE_LINES = [ { id: 'primary', label: 'Primary retention', color: 'var(--ink)' }, { id: 'qs', label: 'Quota-share treaty', color: 'var(--navy)' }, { id: 'xol', label: 'Excess-of-loss layers', color: 'var(--navy-soft)' }, { id: 'cat', label: 'Cat reinsurance', color: 'var(--red)' }, { id: 'param', label: 'Parametric trigger', color: 'var(--amber)' }, { id: 'alt', label: 'Alt-capital sidecar', color: 'var(--green)' }, ]; const CONSTRAINTS = [ { id: 'rbnz', label: 'RBNZ solvency margin', desc: 'Insurance (Prudential Supervision) Act 2010' }, { id: 'ifrs', label: 'IFRS 17 risk-adjustment confidence' }, { id: 'xrb', label: 'XRB climate disclosure' }, { id: 'cap', label: 'Treaty capacity ceiling' }, { id: 'eth', label: 'Constitutional ethics: no orphaning of cover' }, ]; function InverseDesign() { const [tgtPrem, setTgtPrem] = React.useState(15); // % reduction const [tgtCap, setTgtCap] = React.useState(70); // capital efficiency target const [tgtTail, setTgtTail] = React.useState(0.4); // 1-in-X tail tolerance, 0..1 const [tgtReg, setTgtReg] = React.useState(0.6); // regulatory headroom const [iter, setIter] = React.useState(0); const [running, setRunning] = React.useState(false); // Committed targets — only update when the optimiser runs. The grade & stack // are derived from these, not from the live sliders. const [committed, setCommitted] = React.useState({ tgtPrem: 15, tgtCap: 70, tgtTail: 0.4, tgtReg: 0.6, runId: 0, }); const dirty = (tgtPrem !== committed.tgtPrem) || (tgtCap !== committed.tgtCap) || (tgtTail !== committed.tgtTail) || (tgtReg !== committed.tgtReg); // Deterministic "inverse design" — driven by COMMITTED targets only, // so the recommended stack and the grade reflect the last optimiser run. const alloc = React.useMemo(() => { const { tgtPrem, tgtCap, tgtTail, tgtReg } = committed; const primary = clamp(0.55 - tgtPrem * 0.018 + (1 - tgtTail) * 0.15, 0.05, 0.7); const qs = clamp(0.18 + tgtPrem * 0.006 - tgtCap * 0.0015, 0.05, 0.4); const xol = clamp(0.12 + tgtTail * 0.18 - tgtReg * 0.05, 0.04, 0.35); const cat = clamp(0.06 + tgtTail * 0.22, 0.02, 0.35); const param = clamp(0.04 + tgtPrem * 0.004 + (1 - tgtReg) * 0.06, 0.0, 0.25); const alt = clamp(0.05 + (tgtCap / 100) * 0.18 - tgtTail * 0.05, 0.0, 0.30); const arr = { primary, qs, xol, cat, param, alt }; const sum = Object.values(arr).reduce((a,b)=>a+b, 0); Object.keys(arr).forEach(k => arr[k] = arr[k] / sum); return arr; }, [committed]); // Constitutional scores — also from committed values only. const scores = React.useMemo(() => { const { tgtPrem, tgtCap, tgtTail, tgtReg } = committed; const premN = tgtPrem / 35; const capN = (tgtCap - 40) / 55; return { rbnz: clamp(0.50 + alloc.cat * 1.6 + alloc.xol * 1.1 - premN * 0.35 + capN * 0.08, 0, 1), ifrs: clamp(0.45 + alloc.qs * 1.0 + alloc.xol * 0.7 + tgtReg * 0.30 - premN * 0.15, 0, 1), xrb: clamp(0.40 + alloc.param * 1.8 + alloc.cat * 0.5 + tgtReg * 0.10, 0, 1), cap: clamp(0.90 - alloc.qs * 0.7 - alloc.xol * 0.5 + alloc.alt * 0.6 - capN * 0.15, 0, 1), eth: clamp(0.55 + alloc.primary * 0.6 + alloc.cat * 0.4 - alloc.alt * 0.5 - tgtTail * 0.10, 0, 1), }; }, [alloc, committed]); const overallScore = Object.values(scores).reduce((a,b)=>a+b,0) / Object.keys(scores).length; const gradeColor = overallScore > 0.75 ? 'var(--green)' : overallScore > 0.55 ? 'var(--amber)' : 'var(--red)'; const grade = overallScore > 0.85 ? 'A' : overallScore > 0.75 ? 'B+' : overallScore > 0.65 ? 'B' : overallScore > 0.55 ? 'C' : 'D'; // pretend optimisation iterations — commits the live targets at the end const runOptimise = () => { setRunning(true); setIter(0); let n = 0; const id = setInterval(() => { n++; setIter(n); if (n >= 18) { clearInterval(id); setRunning(false); setCommitted({ tgtPrem, tgtCap, tgtTail, tgtReg, runId: committed.runId + 1 }); } }, 80); }; const Slider = ({ label, value, onChange, min, max, step, unit, hint }) => (
{label}
{typeof value === 'number' && value < 1 ? value.toFixed(2) : value}{unit}
onChange(parseFloat(e.target.value))} className="slider red" />
{hint}
); // bar segments let cumX = 0; const totalW = 100; const segs = COVERAGE_LINES.map(c => { const w = alloc[c.id] * totalW; const seg = { ...c, x: cumX, w }; cumX += w; return seg; }); return (
04 / 06 The methodology, applied

Forward modelling is commodity. Inverse design is rare.

Verisk, RMS, Moody's, Milliman, Willis Re — given a portfolio and a hazard set, produce a loss distribution. Mature market. What almost nobody offers commercially is the inverse: given a desired outcome, find the boundary conditions that produce it.

{/* the equation */}
Inverse design equation
∂*  =  argmin∂  {'{'}  ‖ ∫∂ [Φ × λ × S] dA  −  B* ‖²  +  R(∂)  {'}'}
Given a target B* (the desired risk profile), find the optimal boundary configuration ∂ — the coverage stack, mitigation portfolio, treaty allocation — subject to regularisation R(∂) capturing regulatory and physical constraints.
{/* targets */}
Target outcome B*
{dirty && !running && (
Targets changed — re-run optimiser to update boundary ∂* and grade.
)}
{/* output: stack + scores */}
{/* stack */}
Recommended boundary ∂*
iter {iter} · cost ‖.‖² = {(0.42 - iter*0.012).toFixed(3)}
{/* stacked bar */}
{segs.map(s => (
))}
{/* legend rows */} {COVERAGE_LINES.map(c => ( ))}
{c.label} {(alloc[c.id]*100).toFixed(1)}%
{/* constitutional score */}
Constitutional scoring · R(∂)
Boundary configuration evaluated against five regularisation constraints.
{grade}
{(overallScore*100).toFixed(0)} / 100
{CONSTRAINTS.map(c => { const v = scores[c.id]; const col = v > 0.75 ? 'var(--green)' : v > 0.55 ? 'var(--amber)' : 'var(--red)'; return (
{c.label}
{(v*100).toFixed(0)}
); })}
Audit trail: every iteration's configuration, score, and rejection reason is logged and signed. The output of inverse design is not a recommendation — it is a defensible analysis surface for the underwriter and the appointed actuary to interrogate.
); } window.InverseDesign = InverseDesign;