By Myung Jun Kim, Hyeontae Jo & Bong-Gyu Jang

This paper studies optimal portfolio choice for a pension fund with inflation-linked liabilities under regime-switching market dynamics. We consider a fund manager who invests in stocks, inflation-indexed bonds (IIBs), and a risk-free asset to maximize expected utility of the terminal funding ratio, subject to a Value-at-Risk (VaR) constraint. Asset returns and inflation expectations follow a two-state Markov chain representing high and low inflation regimes. The main methodological challenge is solving the constrained optimization problem when option prices-embedded in the VaR constraint-depend on the entire path of regime realizations. We address this by extending the option-based approach of Kraft and Steffensen (2013) with occupation time densities, which reduce the path-dependent pricing problem to a one-dimensional integral over time spent in each regime. This yields semi-closed-form solutions for optimal allocations that adapt dynamically to both funding status and the prevailing inflation environment. Our numerical analysis reveals three main findings. First, optimal allocations exhibit a modified U-shaped pattern: total risky investment exceeds 140% at low funding ratios, drops to approximately 60% near the target as managers lock in gains, and converges to unconstrained Merton weights for well-funded plans. Second, portfolio composition is strongly regime-dependent-IIB allocations exceed stocks by a factor of nearly three in high-inflation regimes, while stocks dominate in low-inflation regimes. Ignoring regime dynamics leads to IIB underweighting of over 30 percentage points. Third, expected inflation is the dominant driver of allocations: a 20% increase shifts IIB allocation by approximately 65 percentage points, whereas risk aversion and correlation effects are comparatively modest. These results highlight the importance of regime-aware dynamic strategies for pension funds managing inflation-linked obligations.

Source SSRN