Modelling Risk

20 February 2026 5 Rivers Capital Research

Stochastic Modelling in Litigation Finance: Making Uncertainty Visible

Legal finance requires decisions to be made before a dispute has reached its conclusion.

A funder assessing a matter may have a view on the strength of the legal case, the potential amount recoverable, how long the dispute may take, what further procedural stages may arise and whether an eventual judgment or award can be converted into cash. None of those questions is necessarily resolved at the point when capital is being considered.

That makes uncertainty central to the analysis.

A conventional approach can reduce that uncertainty to a single expected value: an assumed probability of success multiplied by an assumed recovery, adjusted for time and cost.

That number can be useful. But it can also conceal much of what matters.

Stochastic modelling provides another way to frame the problem. Rather than asking only “What is this claim worth?”, it asks:

What outcomes are possible, how are they connected, when might they occur and which assumptions have the greatest effect on the result?

The purpose is not to predict the decision of a court or tribunal. It is to make uncertainty visible enough to analyse.

A legal claim contains several different uncertainties

A contingent legal claim is not uncertain in only one respect.

There may first be uncertainty about liability: whether the court or tribunal will accept the legal and factual case being advanced.

Even where liability is established, there may be separate uncertainty about quantum. The amount ultimately awarded can depend on evidence, causation, mitigation, valuation methodology, interest and other issues that are distinct from the liability analysis.

Then there is procedure.

A claim can pass through jurisdictional questions, interim applications, hearings, challenges, appeals, settlement discussions and other stages. Each can affect both the eventual outcome and the time required to reach it.

A favourable judgment or award introduces another question: realisation.

An entitlement on paper and cash received are not necessarily the same thing. Recovery can depend on the counterparty's financial position, asset location, enforcement strategy, further proceedings and the cost and time involved in collection.

Running through all of these is time.

A recovery received in eighteen months and the same nominal recovery received several years later do not represent the same economic outcome.

The analytical difficulty is that these uncertainties are also connected.

Enforcement matters only on paths in which an enforceable entitlement exists. Quantum becomes relevant only if the claim reaches the appropriate stage. Costs may depend on how far the matter progresses.

So the uncertainty is not simply a list of variables.

It has a structure.

Why a single probability can hide the structure

Consider a deliberately simple illustration.

Suppose four sequential events must occur before cash is realised, and each is assigned an illustrative 90% probability.

Individually, each assumption may appear relatively strong.

But the probability of completing the entire path is:

90% × 90% × 90% × 90% ≈ 66%

Illustrative only. These probabilities are not calibrated to litigation outcomes.

The example does not tell us anything about the probability of success in an actual dispute.

What it demonstrates is the effect of conditionality.

A claim may look different when the analysis separates the questions that must be answered along the path rather than compressing them into one global assessment.

A simplified structure might distinguish:

whether the claim reaches the relevant decision stage;
whether liability is established;
the range of possible quantum outcomes;
whether the decision survives any relevant challenge;
how much is eventually recovered;
how long the path takes.

This decomposition has an important practical benefit.

It localises disagreement.

Two analysts who disagree about whether a claim is “worth ₹X” have only a conclusion to debate.

If the claim is decomposed, they may discover that they agree on the legal merits and potential quantum but disagree substantially about enforcement. Or they may agree on recovery but use different assumptions about duration.

The disagreement becomes identifiable.

That can be more useful than the headline valuation itself.

From a point estimate to a distribution

Once the claim is decomposed, the next step is to recognise that several inputs may themselves be better represented as ranges or distributions rather than single numbers.

Let X represent realised recovery.

A point estimate might summarise the claim using:

E[X]

the expected recovery across the possible outcomes.

Expected value is useful, but it is only one description of the distribution.

Time is uncertain too

Timing is often handled through a single estimate: perhaps three years, four years or five years.

But duration can itself be modelled as uncertain.

One approach is time-to-event analysis, commonly used where the question is not simply whether an event occurs but when it occurs.

The basic idea is intuitive.

A model can ask:

Given that a matter has remained unresolved until today, what does the assumed process imply about the likelihood of resolution from this point onward?

Different assumptions can produce different duration profiles even when they share the same average or median.

This is relevant because time interacts with the economics of a claim.

Discounting generally reduces the present value of later cash flows. Interest, where applicable, can increase the nominal amount over time. Additional procedural stages can create further expenditure.

The relevant analytical question is therefore not simply:

How long will the matter take?

It is:

How does uncertainty in time interact with the possible recovery paths?

A deeper treatment of survival analysis, hazard rates and duration modelling deserves its own article. At the level of the claim model, the important point is that time does not have to be treated as a fixed assumption.

Simulation turns assumptions into possible paths

Once several uncertain variables interact, the model can become difficult to evaluate using a single formula.

Monte Carlo simulation offers one way to address this.

The basic process is straightforward.

The model specifies the possible states and the assumptions governing them. It then generates one possible path:

one liability outcome;
one quantum outcome;
one procedural duration;
one challenge outcome;
one enforcement outcome.

That path produces one modelled cash flow.

The process is repeated many times.

The result is not a prediction of what will happen. It is a distribution of what happens inside the model under the assumptions that have been specified.

That distinction is important.

More simulation does not mean more certainty

Running 100,000 simulations rather than 10,000 can produce a more numerically stable estimate of the model's output.

It does nothing to establish whether the assumptions entering the model are correct.

If the assumed liability probability is weakly founded, more computing power does not improve it.

If an important procedural path has been omitted, additional simulations will not discover it.

Simulation propagates assumptions. It does not validate them.

This is one of the most important distinctions in quantitative claim analysis.

Sensitivity can matter more than the central estimate

A model may produce a central valuation, but another output can be equally important:

What makes that valuation change?

Sensitivity analysis examines the effect of changing assumptions.

For example:

How does the result change if expected duration increases?
What happens if enforcement recovery is lower?
How sensitive is the outcome to the liability assessment?
Does changing the assumed dependence between claims materially alter a portfolio result?

If a small change in one assumption produces a large change in the result, the model has identified an area of analytical fragility.

That can inform where additional diligence may be useful.

This also introduces a distinction between two forms of uncertainty.

Simulation uncertainty comes from estimating the model's output using a finite number of simulated paths. More computation can reduce it.

Parameter uncertainty comes from uncertainty about the inputs themselves.

More computation cannot remove that.

There is also model risk: the possibility that the structure being simulated is incomplete or inappropriate.

A model can be mathematically precise and still represent the wrong problem.

Precision about a model is not the same thing as certainty about the world.

Data and AI can strengthen the analytical infrastructure

Stochastic modelling ultimately depends on information.

Potential inputs can include procedural histories, claim and award amounts, durations between stages, challenge outcomes, enforcement information, counterparty characteristics and other dispute-related data.

But legal information is often contained in unstructured documents rather than neatly organised datasets.

This is where natural language processing and large language models can be useful.

They can assist with tasks such as:

retrieving relevant information across large document sets;
extracting dates, amounts and procedural events;
constructing chronologies;
organising matters into consistent categories;
identifying potentially comparable documents or matters;
flagging inconsistencies or missing information.

These applications can make information easier to structure and analyse.

But they do not eliminate the distinction between extracting information and predicting an outcome.

A useful hierarchy is:

Retrieval → Extraction → Structuring → Description → Association → Generalisation → Prediction

Each step requires additional evidence.

Extracting the date of an order from a judgment can be checked directly against the source.

Describing what occurred in a corpus of judgments requires confidence in how that corpus was assembled.

Using patterns within that corpus to estimate the outcome of a new matter requires another set of assumptions about comparability, stability and calibration.

In other words:

Extraction is not prediction.

Technology can improve the analytical process without needing to claim that it can forecast the decision of a court or tribunal.

What stochastic modelling ultimately contributes

The strongest case for stochastic modelling in litigation finance is not that it produces a more sophisticated number.

It is that it makes the reasoning behind the number easier to examine.

A structured model can:

separate legal merits from quantum;
distinguish an award from realised recovery;
represent time explicitly;
identify conditional dependencies;
show how different assumptions affect the result;
expose where a conclusion is fragile;
allow assumptions to be revised as new information becomes available.

Most importantly, it can turn a disagreement about a conclusion into a discussion about the assumptions producing it.

There are also clear limits.

A model cannot determine the result of an individual dispute.

It cannot convert professional judgement into observed fact.

It cannot make a weak assumption stronger by simulating it more precisely.

And it cannot validate itself simply because its output appears mathematically coherent.

The better way to think about a stochastic claim model is as a structured argument about uncertainty.

The output matters, but so do the assumptions, the evidence supporting them and the extent to which the conclusion changes when those assumptions change.

The objective is therefore not a more confident estimate.

It is a more transparent analysis.

Illustrative numerical examples in this article are hypothetical and are included solely to explain analytical mechanics. They are not calibrated to any actual claim or portfolio and should not be interpreted as empirical statements about dispute outcomes.

5 Rivers Capital publishes research on the valuation of legal claims as an asset class. This note is analytical and is not investment advice, legal advice, or an offer or solicitation in respect of any security or fund interest. Any figures shown are illustrative and are not calibrated to any actual claim.