Dynamic model of BSF portfolio management

Objectives. The work compares studies on BSF portfolios consisting of a risk-free Bond (B) asset, a Stock (S), and a cash Flow (F) that represents risky asset prices in the form of a tree structure. On the basis of existing models for managing dynamic investment portfolios, the work develops a dynamic model for managing a BSF portfolio that combines risk-free and risky assets with a deposit. Random changes in the prices of a risky asset are reflected in the developed model according to a tree structure. Two approaches to portfolio formation are proposed for the study: (1) initial capital is invested in a risk-free asset, while management is conducted at the expense of a risky asset; (2) the initial capital is invested in a risky asset, but management is carried out at the expense of a risk-free asset.

Methods. A binomial model was used to predict the prices of risky assets. Changes in risky asset prices in the model are dynamically managed via a branching tree structure. A comparative analysis of modeling results reveals the optimal control method.

Results. A dynamic model for unrestricted management of a BSF portfolio has been developed. By presenting risky asset prices according to a tree structure, the model can be used to increase the accuracy of evaluating investments by from 2.4 to 2.7 times for the first approach and from 1.7 to 2.7 times for the second. The increased accuracy of evaluating investments as compared with previously proposed models is achieved by averaging prices at various vertices of the tree.

Conclusions. The results of the research suggest that the use of a dynamic management model based on a tree-like price structure can significantly increase the accuracy of evaluating investments in an investment portfolio.

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