| Abstract: |
| In this paper, we provide a stochastic linear-quadratic (LQ, for short) control approach to the
portfolio choice model introduced by Garleanu and Pedersen (2016).
We first solve the original model in Garleanu and Pedersen ( 2016) by
the classical stochastic LQ control theory in infinite horizon.To capture the present bias, we then generalize the model to the case with non-constant discounting, which is an infinite-horizon time-inconsistent stochastic LQ optimal control problem with nonhomogeneous terms. With the dynamic game point of view, we rigorously develop an approach to finding the so-called equilibrium trading intensity, which is time-consistent and satisfies the local optimality. The solvability of the associated equilibrium algebra quasi-Riccati equations and infinite-horizon extended backward stochastic Volterra integral equations are established. |
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