Loan Limit Optimization

A comprehensive operations research solution for optimizing loan limit increase allocations across customer risk tiers to maximize profitability while managing portfolio risk.

Problem Statement

The objective is to determine how to allocate loan limit increases across different customer segments to maximize customer retention, lifetime value, and profitability—while ensuring regulatory compliance and capital efficiency constraints are met.

Project Structure

Loan_Limit_optimization/
├── loan_limit_optimization.ipynb    # Main analysis notebook (6 modules)
├── loan_limit_increases.csv         # Source data (30,000 customer records)
├── requirements.txt                 # Python dependencies
├── README.md                        # This file
└── output/
    ├── preprocessed_data.csv        # Cleaned dataset
    ├── Loan_Limit_Optimization_Report.docx  # Final report
    ├── module1_output/              # EDA visualizations
    ├── module2_output/              # Markov model outputs
    ├── module3_output/              # Demand forecasts
    ├── module4_output/              # Monte Carlo simulation results
    ├── module5_output/              # Optimization results
    └── module6_output/              # Executive summary and recommendations

Methodology

The analysis follows a six-module framework:

Module 1: Data Preprocessing & Exploratory Analysis

• Data cleaning and validation
• Payment segment analysis
• K-means clustering for customer segmentation
• Key Finding: Uniform ~50% default rate across all segments indicates existing policy is not risk-based

Module 2: Markov Chain Model for Risk State Transitions

• 4-state risk model (Low, Medium-Low, Medium-High, High Risk)
• Transition probability matrix estimation
• Stationary distribution and expected time in state calculations
• Customer lifetime value by risk tier ($136 - $224)

Module 3: Stochastic Demand Forecasting

• Economic scenario simulation (inflation, unemployment, interest rates)
• Seasonal adjustment factors (0.90 - 1.15)
• Uptake rate modeling by risk tier (45% - 70%)
• Stress testing under adverse conditions

Module 4: Loan Lifecycle Simulation (Monte Carlo)

• 100 simulations over 12-month horizon
• Individual customer journey modeling
• Portfolio NPV distribution (Mean: $5.78M, Std Dev: $19.6K)
• Risk metrics: VaR, percentiles, default rates

Module 5: Optimization Engine

• Constrained optimization using SLSQP algorithm
• Objective: Maximize NPV
• Constraints: Default rate ≤ 50%, allocation bounds (10%-40%), capacity (16,000/month)
• Result: 40/40/10/10 allocation across tiers, +3.2% NPV improvement

Module 6: Results & Reporting

• Executive dashboard
• Implementation roadmap
• Sensitivity analysis
• Risk assessment matrix

Key Parameters

Given (from problem statement)

Parameter	Value
Profit per Increase	$40
Eligibility Threshold	60 days
Max Increases per Year	6
Annual Discount Rate	19%

Assumed (model inputs)

Parameter	Value	Rationale
Monthly Capacity	16,000	Based on demand forecast
Max Portfolio Default Rate	50%	Risk appetite ceiling
Loss Given Default	$120	3x profit per increase
Min/Max Tier Allocation	10%/40%	Portfolio diversification

Results

Optimal Allocation Strategy

Risk Tier	Allocation
Low Risk	40%
Medium-Low Risk	40%
Medium-High Risk	10%
High Risk	10%

Performance Metrics

• Optimized NPV: $5,558,354
• NPV Improvement: +$172,364 (+3.2% vs baseline)
• Weighted Default Rate: 40.0% (within 50% constraint)

Installation

1. Create a conda environment:

conda create -n loan_opt python=3.10
conda activate loan_opt

2. Install dependencies:

pip install -r requirements.txt

3. Launch Jupyter:

jupyter notebook loan_limit_optimization.ipynb

Dependencies

• Python 3.10+
• pandas, numpy
• scipy (optimization)
• scikit-learn (clustering)
• matplotlib, seaborn (visualization)
• python-docx (report generation)

Usage

Run the notebook sequentially from Module 1 through Module 6. Each module:

1. Loads outputs from previous modules
2. Performs analysis
3. Saves results to output/moduleX_output/

The final report is generated in output/Loan_Limit_Optimization_Report.docx.

Operations Research Techniques Used

1. Markov Chains - Customer risk state transitions
2. Stochastic Simulation - Demand forecasting with economic factors
3. Monte Carlo Simulation - Portfolio NPV distribution
4. Constrained Optimization - Allocation under business constraints

Key Insights

1. Historical data showed uniform default rates (~50%) across all payment segments—no predictive power for risk differentiation
2. Shifted from descriptive to prescriptive analytics using theoretical risk models
3. Lower-risk customers generate significantly higher lifetime value ($224 vs $136)
4. Optimal strategy concentrates 80% allocation on lower-risk tiers while maintaining diversification
5. Model is robust to moderate economic shocks based on stress testing

Outputs

All outputs are saved to the output/ directory:

• CSV files: Data exports and summary statistics
• JSON files: Model parameters and results
• PNG files: Visualizations and dashboards
• DOCX: Final comprehensive report

Author

Aishwarya Mukherjee