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This article proposes a model for a defined benefit pension plan to minimize total funding variation while controlling expected total pension cost and funding downside risk throughout the life of a pension cohort. With this setup, we first investigate the plan's optimal contribution and asset allocation strategies, given the projection of stochastic asset returns and random mortality evolutions. To manage longevity risk, the plan can use either the ground-up hedging strategy or the excess-risk hedging strategy. Our numerical examples demonstrate that the plan transfers more unexpected longevity risk with the excess-risk strategy due to its lower total hedge cost and more attractive structure.

We provide a new method, the “MV+CVaR approach,” for managing unexpected mortality changes underlying annuities and life insurance. The MV+CVaR approach optimizes the mean–variance trade‐off of an insurer's mortality portfolio, subject to constraints on downside risk. We apply the method of moments and the maximum entropy method to analyze the efficiency of MV+CVaR mortality portfolios relative to traditional Markowitz mean–variance portfolios. Our numerical examples illustrate the superiority of the MV+CVaR approach in mortality risk management and shed new light on natural hedging effects of annuities and life insurance.

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This paper provides extensions to the application of Markovian models in predicting US recessions. The proposed Markovian models, including the hidden Markov and Markov models, incorporate the temporal autocorrelation of binary recession indicators in a traditional but natural way. Considering interest rates and spreads, stock prices, monetary aggregates, and output as the candidate predictors, we examine the out‐of‐sample performance of the Markovian models in predicting the recessions 1–12 months ahead, through rolling window experiments as well as experiments based on the fixed full training set. Our study shows that the Markovian models are superior to the probit models in detecting a recession and capturing the recession duration. But sometimes the rolling window method may affect the models' prediction reliability as it could incorporate the economy's unsystematic adjustments and erratic shocks into the forecast. In addition, the interest rate spreads and output are the most efficient predictor variables in explaining business cycles.