Labor Income

Optimal annuitization with labor income under age-dependent force of mortality ArXiv ID: 2510.10371 “View on arXiv” Authors: Criscent Birungi, Cody Hyndman Abstract We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consumption, portfolio, and labor supply strategies. Our results show that before retirement, investment behavior increases with wealth until a threshold set by labor supply. After retirement, agents tend to consume a larger portion of their wealth. Two main factors influence optimal annuitization decisions as people get older. First, the agent’s perspective (demand side); the agent’s personal discount rate rises with age, reducing their desire to annuitize. Second, the insurer’s perspective (supply side); insurers offer higher payout rates (mortality credits). Our model demonstrates that beyond a certain age, sharply declining survival probabilities make annuitization substantially optimal, as the powerful incentive of mortality credits outweighs the agent’s high personal discount rate. Finally, post-retirement labor income serves as a direct substitute for annuitization by providing an alternative stable income source. It enhances the financial security of retirees. ...

Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning ArXiv ID: 2312.02943 “View on arXiv” Authors: Unknown Abstract This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent’s option to choose when to acquire life insurance for bequest purposes. We examine two scenarios: one with a fixed bequest amount and another with a controlled bequest amount. Applying duality theory and addressing free-boundary problems, we analytically solve both cases, and provide explicit expressions for value functions and optimal strategies in both cases. In the first scenario, where the bequest amount is fixed, distinct outcomes emerge based on different levels of risk aversion parameter $γ$: (i) the optimal time for life insurance purchase occurs when the agent’s wealth surpasses a critical threshold if $γ\in (0,1)$, or (ii) life insurance should be acquired immediately if $γ>1$. In contrast, in the second scenario with a controlled bequest amount, regardless of $γ$ values, immediate life insurance purchase proves to be optimal. Finally, we extend the analysis to consider a scenario in which the individual earmarks part of her initial wealth for inheritance, where a critical wealth threshold consistently emerges. ...