This paper analyzes optimal portfolio allocation in defined contribution pension schemes under joint exposure to mortality and financial jump risks. We develop a continuous-time framework in which both mortality intensity and financial asset prices follow jump-diffusion dynamics, extending standard pension models with continuous mortality and diffusion-based markets. The member's objective combines expected terminal wealth maximization with downside risk control via Conditional Value-at-Risk (CVaR), generating a time inconsistent stochastic control problem. We reformulate the problem as a bilevel optimization structure: for a fixed CVaR threshold, the inner problem reduces to a standard stochastic control problem, while the outer problem becomes a one-dimensional convex minimization. Using inf-convolution regularization and a probabilistic gradient representation derived from Feynman-Kac theory, we establish existence, uniqueness, and differentiability properties of the value function, thereby ensuring analytical tractability of the model. These results provide a rigorous foundation for numerical implementation through semi-Lagrangian schemes combined with gradient-based optimization. Numerical experiments quantify the impact of mortality jumps and mortality-linked derivatives on optimal portfolio policies. In particular, short-maturity longevity derivatives enhance downside protection, and appropriately structured hedging of mortality jump risk improves tail risk measures without reducing expected terminal wealth.
This paper extends the class of semi-structural New Keynesian models to jointly estimate the potential GDP hysteresis elasticity ([[EQUATION]]) and the NAIRU hysteresis elasticity ([[EQUATION]]) across 30 economies via Bayesian methods. Prior distributions for both parameters are elicited through a meta-analysis of existing literature. The cross-country posterior averages are 0.45 for [[EQUATION]] and 0.43 for [[EQUATION]]), implying that, on average, roughly 45% of the prevailing output gap is absorbed into potential output each period; cumulatively, the estimated dynamics imply that about two-thirds of a temporary demand shock remains in GDP at the ten-year horizon. Substantial heterogeneity exists across economies: [[EQUATION]] ranges from 0.25 in Korea to 0.71 in Spain, with European economies displaying systematically higher hysteresis than non-European ones. Cross-country variation in both elasticities is partially explained by labour market institutions, supporting insider-outsider theories. Using the identified demand shocks, local projections reveal that hysteresis operates primarily through persistent employment and capital accumulation effects, consistent with AK-type endogenous growth mechanisms rather than TFP or human capital channels. These findings imply that the costs of recessions and aggressive disinflation are substantially higher than conventional frameworks suggest.
