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This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect Gompertz law and investment opportunities are constant. Healthcare slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. Optimal consumption and healthcare imply an endogenous mortality law that is asymptotically exponential in the old-age limit, with lower growth rate than natural mortality. Healthcare spending steadily increases with age, both in absolute terms and relative to total spending. The optimal stochastic control problem reduces to a nonlinear ordinary differential equation with a unique solution, which has an explicit expression in the old-age limit. The main results are obtained through a novel version of Perrons method.
This paper solves the optimal investment and consumption strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with model uncertainty. The market incompleteness arises from investment constraints of the agent, whil
We extend the result of our earlier study [Angoshtari, Bayraktar, and Young; Optimal consumption under a habit-formation constraint, available at: arXiv:2012.02277, (2020)] to a market setup that includes a risky asset whose price process is a geomet
This paper studies the retirement decision, optimal investment and consumption strategies under habit persistence for an agent with the opportunity to design the retirement time. The optimization problem is formulated as an interconnected optimal sto
We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small transaction costs
In this article we solve the problem of maximizing the expected utility of future consumption and terminal wealth to determine the optimal pension or life-cycle fund strategy for a cohort of pension fund investors. The setup is strongly related to a