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This paper considers a life-time consumption-investment problem under the Black-Scholes framework, where the investors consumption rate is subject to a lower bound constraint that linearly depends on the investors wealth. Due to the state-dependent control constraint, the standard stochastic control theory cannot be directly applied to our problem. We overcome this obstacle by examining an equivalent problem that does not impose state-dependent control constraint. It is shown that the value function is a third-order continuously differentiable function by using differential equation approaches. The feedback form optimal consumption and investment strategies are given. According to our findings, if the investor is more concerned with long-term consumption than short-term consumption, then she should, regardless of her financial condition, always consume as few as possible; otherwise, her optimal consumption strategy is state-dependent: consuming optimally when her financial condition is good, and consuming at the lowest possible rate when her financial situation is bad.
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
This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optima
We propose a new optimal consumption model in which the degree of addictiveness of habit formation is directly controlled through a consumption constraint. In particular, we assume that the individual is unwilling to consume at a rate below a certain
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
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