PINNs

This course is designed to provide a deep understanding of Physics-Informed Neural Networks (PINNs) and their applications in the Finance & Insurance industries. Participants will learn how to integrate mathematical models and domain knowledge into neural network architectures, enabling them to solve complex problems in financial modeling, risk assessment, and actuarial science. The course covers the theoretical foundations of PINNs, as well as practical implementation strategies and case studies tailored to the specific challenges and requirements of the Finance & Insurance industries.

• Understand the theoretical foundations and advantages of Physics-Informed Neural Networks in the context of Finance & Insurance

• Formulate and implement PINNs for solving PDEs and stochastic differential equations (SDEs) relevant to financial modeling and risk assessment

• Incorporate domain knowledge and mathematical constraints into neural network architectures for finance and insurance applications

• Apply PINNs to solve forward and inverse problems in option pricing, portfolio optimization, and actuarial valuation

• Evaluate and interpret the performance of PINN models using appropriate metrics and visualization techniques

• Develop and deploy PINN-based solutions for real-world problems in the Finance & Insurance industries

1. Introduction to PINNs for Finance & Insurance

• Overview of PINNs and their advantages over traditional numerical methods in finance and insurance

• Mathematical formulation of PINNs for solving PDEs and SDEs in financial modeling and risk assessment

• Comparison of PINNs with other machine learning approaches used in Finance & Insurance

• Hands-on exercises: Implementing a basic PINN for solving a simple financial PDE (e.g., Black-Scholes equation)

2. PINNs for Option Pricing and Hedging

• Governing equations in option pricing theory (e.g., Black-Scholes, Heston, jump-diffusion models)

• Formulating PINNs for pricing and hedging options with various payoff structures and market conditions

• Incorporating market data and calibration techniques into PINN-based option pricing models

• Hands-on exercises: Developing PINN models for pricing and hedging exotic options

3. PINNs for Portfolio Optimization and Risk Management

• Formulating PINNs for mean-variance portfolio optimization and asset allocation problems

• Incorporating transaction costs, liquidity constraints, and risk measures (e.g., VaR, CVaR) into PINN-based portfolio optimization models

• Applying PINNs to estimate and forecast market risk factors (e.g., volatility, correlations)

• Hands-on exercises: Implementing PINN models for portfolio optimization and risk assessment

4. PINNs for Actuarial Valuation and Insurance Pricing

• Governing equations in actuarial science (e.g., life contingencies, loss reserving, ruin theory)

• Formulating PINNs for actuarial valuation and insurance pricing problems

• Incorporating mortality tables, claim data, and policyholder behavior into PINN-based actuarial models

• Hands-on exercises: Developing PINN models for pricing life insurance and annuity products

5. Deployment and Future Directions in Finance & Insurance

• Deploying PINN models in production environments for finance and insurance applications

• Strategies for model validation, testing, and maintenance in Finance & Insurance

• Regulatory considerations and model risk management for PINN-based solutions

• Future research directions and open challenges in PINNs for Finance & Insurance industries

• Hands-on exercises: Deploying a PINN model for a finance or insurance use case and discussing deployment strategies

• Strong understanding of partial differential equations (PDEs), stochastic calculus, and numerical methods

• Proficiency in programming with Python and deep learning frameworks (e.g., TensorFlow, PyTorch)

• Familiarity with financial mathematics, risk management, and actuarial concepts