High-Level System Context Diagram
Executive Summary
The Ergodic Insurance Limits framework analyzes insurance decisions using time-average (ergodic) theory rather than traditional ensemble averages. This approach reveals that insurance can enhance business growth even when premiums exceed expected losses by 200-500%, transforming insurance from a cost center to a growth enabler.
Simplified System Architecture
flowchart LR
%% Simplified Executive View
INPUT[("📊 Market Data<br/>& Configuration")]
BUSINESS[("🏭 Business<br/>Simulation")]
ERGODIC[("📈 Ergodic<br/>Analysis")]
OPTIMIZE[("🎯 Strategy<br/>Optimization")]
OUTPUT[("📑 Reports &<br/>Insights")]
INPUT --> BUSINESS
BUSINESS --> ERGODIC
ERGODIC --> OPTIMIZE
OPTIMIZE --> OUTPUT
%% Styling
classDef inputStyle fill:#e3f2fd,stroke:#0d47a1,stroke-width:3px,font-size:14px
classDef processStyle fill:#f3e5f5,stroke:#4a148c,stroke-width:3px,font-size:14px
classDef outputStyle fill:#e8f5e9,stroke:#1b5e20,stroke-width:3px,font-size:14px
class INPUT inputStyle
class BUSINESS,ERGODIC,OPTIMIZE processStyle
class OUTPUT outputStyle
Key Innovation: By comparing time-average growth (what one business experiences over time) with ensemble-average growth (statistical average across many businesses), the framework demonstrates that insurance fundamentally transforms the growth dynamics of volatile businesses.
System Architecture Overview (Detailed)
The actual implementation follows a sophisticated multi-layer architecture:
graph TB
%% Input Layer
subgraph Inputs["📥 Input Layer"]
CONF["Configuration<br/>(YAML/JSON)"]
HIST["Historical Loss Data"]
PARAMS["Business Parameters"]
end
%% Core Simulation
subgraph Core["⚙️ Core Simulation Engine"]
MANU["WidgetManufacturer<br/>(Business Model)"]
CLAIM["ClaimGenerator<br/>(Loss Events)"]
INS["InsuranceProgram<br/>(Coverage Tower)"]
SIM["Simulation Engine<br/>(Time Evolution)"]
end
%% Analysis Layer
subgraph Analysis["📊 Analysis & Optimization"]
MONTE["Monte Carlo Engine<br/>(10,000+ paths)"]
ERGODIC["Ergodic Analyzer<br/>(Time vs Ensemble)"]
OPT["Business Optimizer<br/>(Strategy Selection)"]
SENS["Sensitivity Analysis<br/>(Parameter Impact)"]
end
%% Output Layer
subgraph Outputs["📤 Output & Insights"]
EXCEL["Excel Reports<br/>(Detailed Results)"]
VIZ["Visualizations<br/>(Executive & Technical)"]
METRICS["Risk Metrics<br/>(VaR, CVaR, Ruin Prob)"]
STRATEGY["Optimal Strategy<br/>(Limits & Retentions)"]
end
%% Data Flow
Inputs --> Core
Core --> MONTE
MONTE --> Analysis
Analysis --> Outputs
%% Key Connections
MANU -.-> INS
CLAIM -.-> INS
INS -.-> SIM
SIM -.-> MONTE
ERGODIC -.-> OPT
OPT -.-> SENS
classDef inputClass fill:#e3f2fd,stroke:#1565c0
classDef coreClass fill:#fff3e0,stroke:#ef6c00
classDef analysisClass fill:#f3e5f5,stroke:#7b1fa2
classDef outputClass fill:#e8f5e9,stroke:#2e7d32
class CONF,HIST,PARAMS inputClass
class MANU,CLAIM,INS,SIM coreClass
class MONTE,ERGODIC,OPT,SENS analysisClass
class EXCEL,VIZ,METRICS,STRATEGY outputClass
Reference to System Architecture Diagram
For a visual representation, see: assets/system_architecture.png
The PNG diagram shows the simplified flow, while the detailed architecture above reflects the actual implementation with all major components.
Detailed System Architecture
This diagram shows the overall architecture of the Ergodic Insurance Limits framework, including the main components, external dependencies, and data flow between major modules.
flowchart TB
%% External Inputs and Configurations
subgraph External["External Inputs"]
CONFIG[("Configuration Files<br/>YAML/JSON")]
MARKET[("Market Data<br/>Loss Distributions")]
PARAMS[("Business Parameters<br/>Financial Metrics")]
end
%% Core System Components
subgraph Core["Core Simulation Engine"]
SIM["Simulation<br/>Engine"]
MANU["Widget<br/>Manufacturer<br/>Model"]
CLAIM["Claim<br/>Generator"]
INS["Insurance<br/>Program"]
end
%% Analysis and Optimization
subgraph Analysis["Analysis & Optimization"]
ERGODIC["Ergodic<br/>Analyzer"]
OPT["Business<br/>Optimizer"]
MONTE["Monte Carlo<br/>Engine"]
SENS["Sensitivity<br/>Analyzer"]
end
%% Validation and Testing
subgraph Validation["Validation & Testing"]
ACC["Accuracy<br/>Validator"]
BACK["Strategy<br/>Backtester"]
WALK["Walk-Forward<br/>Validator"]
CONV["Convergence<br/>Monitor"]
end
%% Processing Infrastructure
subgraph Infrastructure["Processing Infrastructure"]
BATCH["Batch<br/>Processor"]
PARALLEL["Parallel<br/>Executor"]
CACHE["Smart<br/>Cache"]
STORAGE["Trajectory<br/>Storage"]
end
%% Reporting and Visualization
subgraph Output["Reporting & Visualization"]
VIZ["Visualization<br/>Engine"]
EXCEL["Excel<br/>Reporter"]
STATS["Summary<br/>Statistics"]
METRICS["Risk<br/>Metrics"]
end
%% Data Flow
CONFIG --> SIM
MARKET --> CLAIM
PARAMS --> MANU
SIM --> MANU
SIM --> CLAIM
SIM --> INS
MANU <--> INS
CLAIM --> INS
SIM --> MONTE
MONTE --> ERGODIC
MONTE --> OPT
ERGODIC --> SENS
OPT --> SENS
MONTE --> ACC
MONTE --> BACK
BACK --> WALK
MONTE --> CONV
CONV --> BATCH
BATCH --> PARALLEL
PARALLEL --> CACHE
CACHE --> STORAGE
ERGODIC --> VIZ
OPT --> VIZ
SENS --> VIZ
STORAGE --> STATS
STATS --> EXCEL
STATS --> METRICS
VIZ --> EXCEL
%% Styling
classDef external fill:#e1f5fe,stroke:#01579b,stroke-width:2px
classDef core fill:#fff3e0,stroke:#e65100,stroke-width:2px
classDef analysis fill:#f3e5f5,stroke:#4a148c,stroke-width:2px
classDef validation fill:#e8f5e9,stroke:#1b5e20,stroke-width:2px
classDef infra fill:#fce4ec,stroke:#880e4f,stroke-width:2px
classDef output fill:#e0f2f1,stroke:#004d40,stroke-width:2px
class CONFIG,MARKET,PARAMS external
class SIM,MANU,CLAIM,INS core
class ERGODIC,OPT,MONTE,SENS analysis
class ACC,BACK,WALK,CONV validation
class BATCH,PARALLEL,CACHE,STORAGE infra
class VIZ,EXCEL,STATS,METRICS output
System Overview
The Ergodic Insurance Limits framework is designed as a modular, high-performance system for analyzing insurance purchasing decisions through the lens of ergodic theory. The architecture follows these key principles:
1. Separation of Concerns
Core Simulation: Handles the fundamental business and insurance mechanics
Analysis Layer: Provides ergodic and optimization capabilities
Infrastructure: Manages computational efficiency and data handling
Validation: Ensures accuracy and robustness of results
Output: Delivers insights through visualizations and reports
2. Data Flow Architecture
Configuration and market data flow into the simulation engine
Simulations generate trajectories processed by analysis modules
Infrastructure layers provide caching and parallelization
Results flow to visualization and reporting components
3. Key Interactions
The Simulation Engine orchestrates the time evolution of the business model
The Manufacturer Model interacts with the Insurance Program for claim processing
Monte Carlo Engine generates multiple scenarios for statistical analysis
Ergodic Analyzer compares time-average vs ensemble-average growth
Batch Processor and Parallel Executor enable high-performance computing
4. External Dependencies
The system integrates with:
NumPy/SciPy for numerical computations
Pandas for data manipulation
Matplotlib/Plotly for visualizations
OpenPyXL for Excel reporting
Multiprocessing for parallel execution