- The paper introduces a novel RL algorithm that formulates insurance portfolio pursuit as a sequential decision-making task using a Markov Decision Process.
- It leverages dynamic programming and k-value computation to adjust prices, achieving an average profit increase of £472 per epoch over traditional approaches.
- The study integrates cost estimation, pricing, and portfolio optimization, offering practical insights and laying the groundwork for future research in long-horizon portfolio management.
Insurance Portfolio Pursuit with Reinforcement Learning
Edward James Young, Alistair Rogers, Elliott Tong, and James Jordon offer an innovative framework for insurance portfolio management in their paper, "Insurance Portfolio Pursuit with Reinforcement Learning". The core contribution of the paper is the formulation of the portfolio pursuit problem as a sequential decision-making task and the introduction of a novel reinforcement learning (RL) algorithm to solve it.
Problem Context and Formulation
Insurance firms face the challenge of determining the optimal offer to make to a customer, balancing between profitability and acceptance probability. Traditionally, this problem is decomposed into cost-estimation and bidding sub-problems. However, the paper distinguishes itself by introducing the portfolio pursuit problem, where an insurance firm seeks to modulate its offers to achieve a predefined target portfolio. This problem is conceptualized as a Markov Decision Process (MDP), and a bespoke RL algorithm is proposed for its resolution.
The paper methodically decomposes the task into four sub-problems: cost-estimation, pricing, portfolio optimization, and portfolio pursuit. The primary focus is on portfolio pursuit, with other sub-problems considered as given. Portfolio pursuit involves adjusting individual customer offers to achieve a target portfolio while ensuring profitability.
Methodology
Novel RL Algorithm
The authors propose a dynamic programming-based RL algorithm that modulates customer prices according to the current portfolio. The algorithm uses a market model, conversion model, and action model. The RL algorithm leverages the BeLLMan optimality equation to determine the optimal policy, which is achieved by computing k-values that guide price modulations.
Value Function Training:
The value function, critical to the RL algorithm, is trained using a next-step value function approach. This involves iteratively approximating portfolio values by sampling from a customer reply buffer and portfolio distributions. A distinctive aspect of the training process is the recentring of value estimates to improve learning stability and focus on differential values between portfolios.
Baseline and Comparison
For comparison, a baseline method mimicking industry practices was developed. This method relies on historical data to adjust offer prices based on the frequency of customer types in the desired portfolio. The baseline method, while reflective of current approaches, lacks the sophistication of the RL algorithm in dynamically adjusting to sequential decision-making contexts.
Experimental Setup and Results
The experiments, conducted in a synthetic market environment, compared the RL algorithm with the baseline approach over eight testing epochs. Each epoch comprised 1000 customer interactions, with performance metrics including profit, portfolio-target loss, and overall reward.
Results:
- Profit: The RL algorithm consistently outperformed the baseline, generating an additional £472 on average per epoch.
- Portfolio Quality: Both methods achieved comparable portfolio-quality metrics.
- Reward: The RL method provided a higher total reward, underscoring its efficacy in balancing profit and adherence to the target portfolio.
Implications and Future Directions
The theoretically grounded and empirically validated RL algorithm presents several implications:
- Practical Value: The algorithm offers a robust solution for dynamically adjusting insurance premiums to achieve strategic portfolio goals, with minimal disruption to existing systems.
- Theoretical Insights: This work extends the applicability of RL to complex, real-world domains, illustrating its potential beyond traditional contexts like trading and game-playing.
Future research may explore:
- Longer Time Horizons: Extending the algorithm to manage portfolios over longer periods, potentially integrating temporal abstraction techniques.
- Customer Exit Modeling: Enhancing the model to account for customer churn, thus requiring more granular portfolio representations.
- Robustness and Adaptivity: Incorporating model uncertainty and facilitating online learning to adapt to changing market conditions.
Conclusion
This paper introduces a sophisticated RL-based methodology for the portfolio pursuit problem in the insurance sector, presenting significant advancements over existing industry practices. By offering a detailed mathematical formulation, comprehensive experimental validation, and highlighting avenues for future work, the authors contribute substantially to the field of insurance pricing and portfolio management. The proposed algorithm's ability to generate higher profits without compromising portfolio quality positions it as a valuable tool for insurance firms in a competitive market.