Optimal investment in DC pension schemes under career-driven wage uncertainty

Abstract

In defined-contribution (DC) pension schemes, members must manage investment risk while ensuring they accumulate sufficient wealth for retirement. At the same time, labor income risk plays a crucial role, as it governs the contribution stream. I study the optimal investment problem of a DC pension fund member in the presence of unhedgeable wage risk driven by idiosyncratic career dynamics. Building on [1], labor income follows a regime-switching process governed by a continuous-time Markov chain; differently from their setting, here the switching states represent ordered career phases (e.g. bad, stagnant, and good) rather than aggregate economic conditions. Contributions are defined as a fixed fraction of such stochastic labor income, and financial investment takes place in a standard Black–Scholes market. The pension fund member maximizes expected utility of terminal wealth under CARA preferences. We solve the problem via dynamic programming and derive closed-form expressions for the value function and the optimal portfolio rule. Due to our use of CARA preferences, the optimal risky allocation is independent of both wealth and labor income. The key implication, however, concerns the impact of career dynamics on retirement outcomes: under a monotone transition structure, we establish stochastic ordering results [2] showing that better initial career phases lead to systematically higher terminal pension wealth. Yet this ranking reverses when performance is measured in relative terms via the replacement ratio: indeed, individuals starting in better career phases tend to achieve lower replacement ratios. This mechanism is consistent with the theoretical insights in [3] and with the empirical evidence documented in [4]. Overall, our results show that career dynamics shape not only wealth accumulation but also pension adequacy, generating persistent and economically meaningful heterogeneity in retirement outcomes even under identical optimal investment policies.