Optimal smoothing mechanism for actuarial discount rate in pension liability valuation in North America

Although academic studies widely accept market-consistent valuation for pension liabilities, this approach can lead to unstable liability values due to market volatility. To address this issue, pension actuaries often employ smoothed actuarial discount rates. Our research focuses on establishing an optimal smoothing mechanism. We formulate an optimization problem that balances two objectives: (1) minimizing unexpected contributions resulting from actuarial liability fluctuations due to discount rate changes, and (2) ensuring actuarial valuations align with the market value of the pension liability. By solving the Hamilton–Jacobi–Bellman equation, we derive an explicit solution. For practical application, we simplify and approximate the solution, resulting in a clear and intuitive smoothing rule to guide pension practitioners.