Over the past 30 years, the theory and practice of financial markets have undergone fundamental changes. Modern mathematical models, computer technologies, financial instruments and mechanisms have formed a new scientific sphere - “financial engineering”. Robert Merton is considered the “founding father” of the concept and content of financial engineering, who introduced the scientific method into finance, using mathematical models and statistical tools to analyze financial markets and assess risks. In the context of financial engineering, the formulation of new mathematical problems of financial resource management, including the modification of target functionals, is of interest. This paper proposes one of the options for such a modification.