Dimension Reduction in Stochastic Optimal Control

Dimension Reduction in Stochastic Optimal Control

While the classical Merton type framework is among the most comprehensively studied and has spurred an extensive theoretical literature, its empirical implementation has been disappointing with a large literature documenting its shortcomings. In particular, its numerical implementation via stochastic dynamic programming has been neglected in the community largely due to the curse of dimensionality. The objective of this project is to explore the recent advances in the statistical community for dimension reduction in such a way that the dimension reduction of the objective functions is aligned with portfolio optimisation in the context of stochastic optimal control setting and ultimately results in a better portfolio performance in a high dimensional investment space.

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Yangzhuoran Yang
Research Assistant

Talks

We introduce the general optimal stochastic control setting in the case of portfolio selection. We implement an Optimal Control Projection Algorithm (OCPA) to solve the objective function while using projection, kernel estimation and solving for a solution in a single index context. In addition, we propose a lower bound of the value function which can be used to test the validity of the estimated sub-optimal. We compare the performance of OCPA and the popular EM algorithm using both the simulation and empirical study. In general, the OCPA is doable when the EM algorithm is not, and the OCPA is much faster and performs better when the EM algorithm is doable.

We introduce the general optimal stochastic control setting in the case of portfolio selection. We propose a two-step algorithm to solve the objective function. At the first step, we utilise the transformation from mean-variance portfolio selection to OLS regression, projecting the assets space into a single portfolio. Then we take the dimension-reduced control space into the single index dynamic programming problem which aims to solve a certain finite time horizon objective function.