Control in the socio-economic systems

Credit leverage optimization maximizing expected rate of portfolio value increase

O. I. Krivosheev<sup>ab

a</sup> Moscow State University of Economics, Statistics and Informatics
^b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Abstract: Considered is a control problem of Markowitz investment portfolio, which is subjected to independent stochastic increments of price logarithm, described by Wiener process with a drift and cash used as the risk free asset. An expression of optimal credit leverage is obtained. Optimal time or a leverage correction threshold is derived under the circumstances of positive transactional costs. Equilibrium asset return and leverage are found under conditions of leveling the equity capital profitability in all markets. The same approach can be adapted to real sector enterprises.

Keywords: CAPM, Wiener process, assets, credit leverage, portfolio, shares, random walks, rate of return.

UDC: 336.76