Multi-period and multi-objective stock portfolio modeling considering cone constraints

Nowadays, one of the major concerns of investors is choosing a realistic stock portfolio and making proper decisions according to an individual's utility level. It is essential to consider two conflicting goals of return and risk for profitability; as a result, balancing the above goals has been identified as an investment concern. This paper modifies and optimizes a multi-objective and multi-period stock portfolio considering cone constraints and uncertain and stochastic discrete decisions. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was used to solve the model due to the issue's complexity. Two objective functions in the model could be explained by maximizing expected returns and minimizing investment risk. The Pareto chart of the problem was drawn, which allows investors to make decisions based on various levels of risk. Another result obtained in this study is calculating the percentage of optimal amounts assigned to each asset, providing a base for investors to avert investing in unsuitable assets and incurring losses. Finally, a sensitivity analysis of essential parameters was performed, which is critical in this issue. According to the results, increasing the number of problem constraints provides a base for the model reaction, and the optimal percentage allocated to each asset varies. Therefore, this prioritizes restrictions in different situations and according to the investors' choice.

Keywords:

Genetic Algorithm , optimization , Stock portfolio , Cone constraints , Multi-objective modeling , Discrete decisions