Two mortality trajectories with identical starting and terminal values can differ in economic consequence by up to 8% of portfolio value. Every traditional model misses this. Eld does not.
Survival is a path-dependent functional.
Actuarial practice treats it as though it is not.
The survival probability ₜpₓ = exp(−∫μₛ ds) depends on the integrated mortality path, not its endpoint. When a mortality spike arrives early — against small reserves — it carries materially different consequences than the same spike arriving late against accumulated capital.
Standard actuarial models assess longevity risk using terminal-value objectives. They cannot distinguish these scenarios. Eld encodes the full path through the log-signature transform from rough path theory, capturing mortality timing, return-reserve correlation, and basis risk exposure that terminal values cannot see.
The result: path-dependent effects worth up to 8% of portfolio value, previously invisible, now priceable in seconds.
Both scenarios: µ₀ = 0.020, µᵀ ≈ 0.020, identical terminal reserves. Yet they are not the same.
Rough path theory encodes your mortality trajectory into log-signature components. Each captures what terminal values cannot: timing, correlation between mortality and reserves, basis risk exposure.
Wasserstein distributionally robust regret optimisation. Hedges against distributional misspecification without the over-conservatism of standard robust methods. Measures performance against the best alternative policy, not absolute worst-case.
Gradients propagate backward through Baker–Campbell–Hausdorff compositions. O(MD²) complexity, independent of the number of controls. GPU-parallel across Monte Carlo paths. The same infrastructure runs both optimisation and hedging.
Quote generation that once required days of actuarial team time completes in seconds. Path-dependent pricing captures timing effects that standard models miss, enabling more accurate premiums and a competitive edge in the PRT market.
Understand the path premium in your own liability portfolio before entering a buy-in negotiation. Know what your trustees are paying for — and what the insurer's terminal-value model cannot see that yours can.
Percentile tranche valuation with path-dependent survival probability computation. The max-affine structure of tranche payoffs maps directly onto Eld's log-signature framework — no approximation required.
API access to Eld's computation engine. Run path-dependent pricing inside your own models. Malliavin-based hedge ratios computed in a single backward pass rather than O(M) forward passes. Full Solvency II internal model documentation.
No sales process. No consulting relationship required. Upload a cohort, run a pricing cycle, see the path premium your current model cannot find.