Density quantization method in the optimal portfolio choice with partial observation of stochastic volatility

TL;DR

This paper introduces a density quantization method to simplify the complex problem of optimal portfolio choice under partial observation of stochastic volatility, enabling more efficient numerical solutions.

Contribution

The paper presents a novel density quantization approach that reduces the infinite-dimensional filtering problem to a finite set, improving computational efficiency in portfolio optimization.

Findings

Density quantization effectively reduces the state space complexity.

The method improves numerical stability and computational speed.

Application to portfolio optimization under stochastic volatility.

Abstract

Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - density quantization - is introduced which reduces the original infinite dimensional state space of the problem to the finite quantization set. The density quantization is embedded into the numerical algorithm to solve the dynamic programming equation related to the portfolio optimization.