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Multi-stage Investments with Real Options

Many investment decisions involve multiple decision stages that have termination options. Information is revealed over time, and the ability to modify behaviour leads to a decision “tree”. Once uncertain outcomes and a changing environment over time are factored in, solving these types of problems becomes very complex. Stochastic Dynamic Programming provides a solution method that will solve these problems.

These models can be used in applications such as mining or oil exploration where testing can reveal better information at some cost.

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A problem with real-world complexity is likely to involve some or all of the following aspects:

  • Multiple decision stages, potentially with termination options. For instance, an oil exploration project may involve seismic surveys, core samples, test wells and the like.
  • Several possible future outlooks possible at each decision stage.
  • Information such as prices or costs are revealed over time. This can affect our view about the profitability of each possible outcome.
  • Multiple projects possible, but with an overall budget or other constraints for all projects combined.
    Once all of these factors are considered, we have a very complex problem.


Stochastic Dynamic Programming is a very efficient method for solving large decision trees in a short period of time. At each combination of decision nexus and possible future state the SDP solver tells us the optimal decision to make.


Our custom-written solver creates the optimal solution for this type of solution in a very short period of time. As well as the optimal “roadmap” of decisions, outputs include such things as expected return, and expected cash flow.