# Optimal Entry and Consumption under Habit Formation

## TL;DR

This paper models the joint problem of optimal entry timing and consumption under habit formation, using stochastic Perron's method to characterize the value function as a unique viscosity solution of variational inequalities.

## Contribution

It introduces a novel framework combining optimal stopping and dynamic consumption under habit formation with partial information, solved via stochastic Perron's method.

## Key findings

- Characterizes the value function as a unique viscosity solution.
- Provides a rigorous mathematical framework for combined entry and consumption decisions.
- Extends existing models by incorporating information costs and habit formation.

## Abstract

This paper studies a composite problem involving the decision making of the optimal entry time and dynamic consumption afterwards. In stage-1, the investor has access to full market information subjecting to some information costs and needs to choose an optimal stopping time to initiate stage-2; in stage-2, the investor terminates the costly full information acquisition and starts dynamic investment and consumption under partial observations of free public stock prices. The habit formation preference is employed, in which the past consumption affects the investor's current decisions. By using the stochastic Perron's method, the value function of the composite problem is proved to be the unique viscosity solution of some variational inequalities.