A Method of Optimal Investment with Stage-by-Stage Conditional Value at Risk (CVaR) Constraints and Known Parameters of Return Vectors

Abstract

The paper investigates a multi-stage investment problem under Conditional Value at Risk (CVaR) constraints with: a given security level for bankruptcy, short selling permission, a normal and an elliptical total return distribution models. The purpose of the work is to find a method of determining the optimal investment in this problem at each stage. As a result of the study, an optimal investment strategy is found and it is shown that the optimal investment portfolio at each stage does not depend on the value of the investor’s capital, but depends only on the number of stage. It is shown that the multi-stage problem can be reduced to a finite number of one-stage optimization problems, which are problems of conic programming. For the one-stage problem, conditions for the non-emptiness of the set of admissible portfolios are given and the Kuhn–Tucker theorem is applied. Additionally, this paper presents a numerical example of finding the optimal investment based on the open data on rates of assert prices of companies on the stock exchange.