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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, while the model uncertainty stems from drift and volatility processes for risky stocks in the financial market. The agent seeks her best and robust strategies via optimizing her robust forward investment and consumption preferences. Her robust forward preferences and the associated optimal strategies are represented by solutions of ordinary differential equations, when there are both drift and volatility uncertainties, and infinite horizon backward stochastic differential equations, coupled with ordinary differential equations, when there is only drift uncertainty.
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
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 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
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
A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion fluctuations. Th