Quincus

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.

LIVE

Run ten thousand paths

Removing the jump term moves the median by 0.83 days and understates breach probability by 19 points.

p505.68d
p9010.26d
p9917.44d
Breach probability21.2%
Modeljump diffusion
Runs in your browser on a simplified version of the production method. Illustrative of behavior, not of production performance.

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

Pr(st+1=jst=i)=pij\Pr(s_{t+1} = j \mid s_t = i) = p_{ij}

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.

Three regime hidden Markov state machineNormalElevatedDisrupted

Jump diffusion

dStSt=(μλκ)dt+σdWt+(Y1)dNt\frac{dS_t}{S_t} = (\mu - \lambda\kappa)\,dt + \sigma\,dW_t + (Y - 1)\,dN_t

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.

Jump diffusion sample path with two visible jumps

Dependence structure

Cθ(u,v)=(uθ+vθ1)1/θC_\theta(u,v) = \left( u^{-\theta} + v^{-\theta} - 1 \right)^{-1/\theta}

A Clayton copula captures lower tail dependence between lanes, because correlated failure is the failure that matters. Independent marginals systematically understate joint disruption.

Clayton copula sample scatter with lower tail clustering

What this changes

What you can now say out loud.

  1. 01

    Plans scored against the distribution, not the mean.

  2. 02

    Tail exposure priced rather than assumed away.

  3. 03

    Scenario testing before capital is committed.

If your network makes decisions under uncertainty, we should talk.

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