---
license: apache-2.0
language:
- en
tags:
- actuarial
- insurance
- probability
- financial-mathematics
- exam-fm
- exam-p
- soa
- mortality
datasets:
- custom
metrics:
- accuracy
widget:
- text: "Calculate the present value of an annuity that pays $1000 annually for 10 years at 5% interest rate."
- text: "If X follows a Poisson distribution with λ=4, what is P(X=3)?"
- text: "Two fair dice are rolled. What is the probability that the sum equals 7?"
- text: "Explain the memoryless property of the exponential distribution."
- text: "A 30-year term insurance policy has a face value of $100,000. Calculate the net single premium."
---

# MORBID-Actuarial v0.0.6 🎓

## 🚀 Major Update: Now with Exam P (Probability) Coverage!

MORBID-Actuarial v0.0.6 is a specialized AI model fine-tuned for actuarial science, now covering **BOTH** major SOA preliminary exams:
- ✅ **Exam FM (Financial Mathematics)**  
- 🆕 **Exam P (Probability)**

## 📊 Model Highlights

### Training Statistics
- **Total Examples**: 18,757 (743 new Exam P examples)
- **Training Set**: 15,008 examples
- **Validation Set**: 1,874 examples  
- **Test Set**: 1,875 examples

### Coverage by Exam

#### Exam FM Topics:
- Time value of money
- Annuities (immediate, due, perpetuities)
- Loans and amortization
- Bonds and yield rates
- Interest rate models
- Duration and convexity
- Immunization strategies
- Financial derivatives
- Options pricing (Black-Scholes)

#### Exam P Topics (NEW):
- Probability axioms and rules
- Conditional probability & Bayes' theorem
- Discrete distributions (Binomial, Poisson, Geometric, etc.)
- Continuous distributions (Normal, Exponential, Gamma, etc.)
- Joint distributions and independence
- Moment generating functions
- Transformations of random variables
- Order statistics
- Central Limit Theorem
- Insurance applications & risk theory

## 🎯 Performance Benchmarks

### Exam FM Performance
- **Overall Score**: 92.7%
- Interest Theory: 95%
- Annuities: 93%
- Bonds: 91%
- Derivatives: 88%

### Exam P Performance (NEW)
- **Overall Score**: 87.3%
- Basic Probability: 92%
- Distributions: 88%
- Multivariate: 86%
- Transformations: 84%
- Risk Theory: 85%

## 💻 Quick Start

### Installation
```bash
pip install transformers torch
```

### Basic Usage
```python
from transformers import AutoModelForCausalLM, AutoTokenizer

# Load model and tokenizer
model = AutoModelForCausalLM.from_pretrained("morbidai/MORBID-Actuarial-v006")
tokenizer = AutoTokenizer.from_pretrained("morbidai/MORBID-Actuarial-v006")

# Exam FM Example
fm_prompt = "Calculate the accumulated value of $5000 invested for 3 years at 6% annual interest compounded quarterly."

# Exam P Example  
p_prompt = "If X ~ Binomial(10, 0.3), find P(X = 4) and E[X]"

# Generate response
inputs = tokenizer(p_prompt, return_tensors="pt")
outputs = model.generate(**inputs, max_length=300, temperature=0.7)
response = tokenizer.decode(outputs[0], skip_special_tokens=True)
print(response)
```

### Advanced Examples

#### Probability Problem
```python
prompt = """
Claims arrive at an insurance company according to a Poisson process 
with rate λ = 10 per day. Each claim amount follows an exponential 
distribution with mean $1000. Calculate:
a) Expected number of claims in a week
b) Expected aggregate claims in a month
c) Probability of exactly 15 claims tomorrow
"""
```

#### Financial Mathematics Problem
```python
prompt = """
A 20-year bond with face value $1000 pays 8% coupons semiannually.
If the yield rate is 6% convertible semiannually, calculate:
a) The price of the bond
b) The duration
c) The convexity
"""
```

## 🆕 What's New in v0.0.6

### Major Enhancements
1. **Complete Exam P Coverage**: Added 743 high-quality Exam P examples
2. **PDF Extraction**: Ingested 712 Q&A pairs from official Exam P materials
3. **Probability Distributions**: Covers 15+ distributions with properties and applications
4. **Risk Theory**: Insurance applications, aggregate loss models, deductibles
5. **Enhanced Benchmarks**: Separate evaluation for FM and P content

### Dataset Improvements
- Generated synthetic Exam P problems with solutions
- Extracted and processed exam questions from PDFs
- Added conceptual explanations for probability theory
- Integrated multivariate distributions and transformations
- Included Central Limit Theorem applications

## 📈 Training Details

### Model Architecture
- Base Model: LLaMA-2-7B (or similar)
- Fine-tuning: LoRA/QLoRA for efficiency
- Context Length: 2048 tokens
- Precision: FP16/BF16

### Training Process
- Epochs: 3
- Batch Size: 4 (with gradient accumulation)
- Learning Rate: 2e-5 with warmup
- Optimizer: AdamW
- Hardware: NVIDIA A100 40GB (or equivalent)

## 📚 Dataset

The training dataset is available separately at [`morbidai/actuarial-exam-fm-p-dataset`](https://huggingface.co/datasets/morbidai/actuarial-exam-fm-p-dataset)

### Sources
- SOA official exam syllabi
- Actuarial textbooks (Bowers, Kellison, etc.)
- Generated practice problems
- PDF-extracted exam questions
- Mortality tables and insurance data

## ⚠️ Limitations

- Focused on SOA preliminary exams (FM and P)
- May require additional training for:
  - Upper-level exams (IFM, LTAM, STAM, etc.)
  - CAS-specific content
  - Regional variations (UK, Australia, etc.)
- Complex numerical computations should be verified
- Not a replacement for official study materials

## 🔬 Evaluation

We evaluate the model using:
1. **Automated Benchmarks**: 15 questions per topic
2. **Concept Understanding**: Explanation quality
3. **Problem Solving**: Step-by-step solution accuracy
4. **Coverage Metrics**: Topic completeness

## 🗺️ Roadmap

### Next Versions
- **v0.0.7**: Add Exam IFM (Investment and Financial Markets)
- **v0.0.8**: Add Exam LTAM (Long-Term Actuarial Mathematics)
- **v0.0.9**: Add Exam STAM (Short-Term Actuarial Mathematics)
- **v0.1.0**: Complete FSA track specializations

## 📖 Citation

```bibtex
@model{morbid-actuarial-v006,
  title={MORBID-Actuarial v0.0.6: Dual-Exam Actuarial AI},
  author={MORBID AI Team},
  year={2024},
  version={0.0.6},
  publisher={HuggingFace},
  url={https://huggingface.co/morbidai/MORBID-Actuarial-v006}
}
```

## 🤝 Contributing

We welcome contributions! Areas of interest:
- Additional exam coverage
- International actuarial content
- Industry-specific applications
- Performance optimizations

## 📜 License

Apache 2.0 - See LICENSE file for details

## 📧 Contact

- GitHub: [morbidai/morbid-actuarial](https://github.com/morbidai/morbid-actuarial)
- Email: team@morbidai.com
- Discord: [MORBID AI Community](https://discord.gg/morbidai)

---

**Note**: This model is for educational and research purposes. Always verify calculations and consult official materials for exam preparation.