Optimal Selection of Investment Portfolios in a Multi-Stage Problem under VaR Constraint on the Stage-by-Stage Investor’s Capital and Bankruptcy

The object of research is investment portfolios and ways to optimize them. The purpose of the work is to develop an investment strategy for constructing optimal investment portfolios in a multistage problem with a VaR constraint on intermediate capital values and the possibility of bankruptcy. It was decided to divide the original problem into a one-stage and multi-stage problem under the given constraints. It was found that a one-stage problem can be solved as a concave programming problem, and a multi-stage problem can be solved as a dynamic programming problem using Bellman functions. The paper also provides an example of calculating optimal portfolios, consisting of the shares of three real companies, using the Python programming language. The results of the work are useful for companies with a long investment horizon, individual investors, as well as portfolio theory researchers who are dealing with VaR constraints.