Analysing Optimal Portfolios Under Uncertainty

This document describes current steps and results in the updated workflow.

1. Sampling multipliers and characteristics
2. Identifying optimal portfolios
3. Identifying Factors Driving Uncertainty

Step 1: Sampling multipliers and characteristics

Each simulation draws every impact multiplier once from its distribution and combines it with each opportunity's characteristic. Together, these give the expected value of each dollar invested in an opportunity in that simulation.

Step 2: Identifying optimal portfolios

For each simulation, we derive an optimal portfolio using linear programming. This process is repeated across numerous simulations to capture variability due to uncertainty.

The solver is also used to identify the optimal portfolio for all simulations combined.

graph LR

%% Outer Subgraph Surrounding All Simulations
subgraph Simulations
    direction LR
    %% Simulation n
    subgraph Simulation n
        direction LR
        SOW1(Multipliers)
        SOO1(Characteristics)
        OP1(Optimal Portfolio)
    end
    SOW1 --> SOO1 --> OP1

    %% Ellipsis to represent continuation
    subgraph  
        ellipsis[•••]
        style ellipsis fill-opacity:0,stroke:none,font-size:30px
    end

    %% Simulation 3
    subgraph Simulation 3
        direction LR
        SOW2(Multipliers)
        SOO2(Characteristics)
        OP2(Optimal Portfolio)
    end
    SOW2 --> SOO2 --> OP2

    %% Simulation 2
    subgraph Simulation 2
        direction LR
        SOW3(Multipliers)
        SOO3(Characteristics)
        OP3(Optimal Portfolio)
    end
    SOW3 --> SOO3 --> OP3



    %% Last Simulation (Simulation n)
    subgraph Simulation 1
        direction LR
        SOWn(Multipliers)
        SOOn(Characteristics)
        OPn(Optimal Portfolio)
    end
    SOWn --> SOOn --> OPn
end

%% Combined Optimal Portfolio for all Simulations
COP(Combined Optimal Portfolio)
Simulations --> COP