Abstract
In this paper, we analyze the optimal consumption and investment problem of an agent by incorporating the stochastic hyperbolic preferences with constant relative risk aversion utility. Using the dynamic programming method, we deal with the optimization problem in a continuous-time model. And we provide the closed-form solutions of the optimization problem.
Highlights
After the seminal research of Strotz [11], the exponential discount function with a constant discount rate has been widely used in finance/economics
Harris and Laibson [4] introduced the instantaneous-gratification (IG) model of time preferences. This model is based on a quasi-hyperbolic stochastic discount function
We suggest a technical approach which is different from Palacios-Huerta and Pérez-Kakabadse [9] and Zou et al [13] for solving an optimal consumption and investment problem with a stochastic hyperbolic discounting function
Summary
After the seminal research of Strotz [11], the exponential discount function with a constant discount rate has been widely used in finance/economics. This model is based on a quasi-hyperbolic stochastic discount function. Palacios-Huerta and Pérez-Kakabadse [9] extended the classical problem of [7, 8] to the time-inconsistent agent problem. Zou et al [13] extended the work of Palacios-Huerta and Pérez-Kakabadse [9] to an agent who has finite life time.
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