Optimization of the bank's loan portfolio taken into account of market risk based on the Lagrange multipliers method

The article considers the problem of forming an optimal portfolio of commercial bank loans. The subject of the study is the mechanism of bank profit formation through lending to individuals. The relevance of the research topic is due to the fact that at present, in the conditions of increasing competition in the financial services market, one of the urgent tasks of banks is the optimization of loan portfolios. One of the ways to solve this problem is to develop a mathematical model that will allow effectively managing the loan portfolio and optimizing financial risks. An optimization model has been developed and statistical data have been analyzed, on the basis of which regression models are compiled, and the limitations taken into account in the model have been analyzed. The conditions for optimizing the bank's loan portfolio are proposed, allowing for maximizing the bank's profit. Optimization models allow choosing such shares of lending types that maximize the bank's total profit from lending to individuals. A set of conditions for the optimal loan portfolio has also been determined, providing a limit on the risk of interest rate volatility, which is one of the types of market risk. The results of numerical experiments on the example of PAO VTB Bank are presented, showing the economic effect of the proposed developments. The obtained results and the developed models of loan portfolio optimization can be used for planning of the banks' activities. The conducted research expands the scientific framework of understanding the importance of applying optimization processes in compiling the loan portfolio by banks.