Optimal strategies for investment and consumption: stochastic analysis with pontryagin's principle under economic uncertainty

Abstract

This study investigates how stochastic optimization is applied to the management of a company's portfolio in order to maximize the expected utility of wealth over a given period. Inspired by Merton's research, this model involves random volatility in the financial markets, while maintaining a constant interest rate to take better account of real economic uncertainties. The aim is to formulate optimal investment and consumption strategies based on Pontryagin's maximum principle. Taking into account key factors such as economic growth and market volatility, as well as risk aversion in our financial considerations, we recommend an approach incorporating a quadratic penalty for excessive investment. This innovative method aims to adjust financial choices in line with economic fluctuations and ensure prudent management of the company's monetary resources. Finally, numerical simulations illustrate the influence of these factors on overall wealth, as well as on investment and consumption, underlining the importance of prudent portfolio management during periods of uncertainty.