M.D. Missarov^∗ , E.P. Shustova^∗∗

Kazan Federal University, Kazan, 420008 Russia

E-mail: ^∗moukadas.missarov@kpfu.ru, ^∗∗evgeniyashustova@yandex.ru

Received July 25, 2019

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DOI: 10.26907/2541-7746.2019.4.543-551

For citation : Missarov M.D., Shustova E.P. Constant rebalancing strategies with minimal risk. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 4, pp. 543–551. doi: 10.26907/2541-7746.2019.4.543-551. (In Russian)

Abstract

The numerical characteristics of constant rebalancing strategies for a portfolio of one riskfree and two risky assets were studied. Constant rebalancing means that the current capital at the end of each period is distributed over all assets of the next period in the same (constant) proportions. In this case, the input and output of the capital from the investment process is not allowed. In the proposed model, the continuous interest rates of risky assets in different periods are independent of each other and determined by the same two-dimensional Gaussian distribution for all periods. An algorithm for constructing the constant rebalancing strategy with a given mathematical expectation of capital at the end of the last period and a minimal variance of this capital was developed.

Keywords: constant rebalancing strategy, continuous interest rates, Gaussian and lognormal two-dimensional distributions, mathematical expectation and variance of terminal capital

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