Stochastic layer
Networks do not fail on average.
The patented core treats disruption as a process with structure rather than as noise. Three model families run underneath the optimizer and feed it distributions.
Run ten thousand paths
Removing the jump term moves the median by 0.83 days and understates breach probability by 19 points.
The problem class
Three ways a network breaks.
Regime rather than noise.
Disruption is a state the network enters, not white noise around a mean. Model the state.
Discontinuity rather than volatility.
Strait closures and demand shocks are jumps. A Gaussian model prices them at zero.
Correlated rather than independent failure.
When one lane goes, its neighbors go too. Independent marginals understate joint risk.
The method
Three model families feed the optimizer.
The patented core treats disruption as a process with structure rather than as noise.
Regime switching
A hidden Markov layer classifies each lane into normal, elevated, or disrupted, and the optimizer receives a different travel time distribution per regime rather than a blended average that describes no actual state of the world.
Jump diffusion
Rate and congestion processes carry a Poisson jump term. Continuous volatility explains an ordinary week. It does not explain a strait closing, and a model without a jump term will price that risk at zero.
Dependence structure
A Clayton copula captures lower tail dependence between lanes, because correlated failure is the failure that matters. Independent marginals systematically understate joint disruption.
What this changes
What you can now say out loud.
- 01
Plans scored against the distribution, not the mean.
- 02
Tail exposure priced rather than assumed away.
- 03
Scenario testing before capital is committed.
Where it runs
Sectors that lean on this capability.
If your network makes decisions under uncertainty, we should talk.
We work with a small number of operators at a time. Tell us what your network is optimizing for.
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