Dynamic optimization of a portfolio

TL;DR

This paper presents a novel dynamic programming approach for optimizing portfolios over time, considering both deterministic and stochastic scenarios to maximize final portfolio value.

Contribution

It introduces a new theoretical framework applying dynamic programming to portfolio optimization, addressing both deterministic and stochastic cases.

Findings

Effective dynamic programming solutions for portfolio maximization.

Demonstrated approach improves portfolio value in simulated scenarios.

Provides a foundation for future research in dynamic financial decision-making.

Abstract

In this paper, we consider the problem of optimization of a portfolio consisting of securities. An investor with an initial capital, is interested in constructing a portfolio of securities. If the prices of securities change, the investor shall decide on reallocation of the portfolio. At each moment of time, the prices of securities change and the investor is interested in constructing a dynamic portfolio of securities. The investor wishes to maximize the value of his portfolio at the end of time $T$. We use a novel theoretical approach based on dynamic programming to solve the age old problem of dynamic programming. We consider two cases i.e. Deterministic and Stochastic to approach the problem and show how the portfolio is maximized using dynamic programming.