Investigation of convergence to the turnpike of deflators in the Cantor-Lippman model of investments in an imperfect capital market

In this work, we use the description of the investor’s individual environment, proposed in the Kantor-Lippman model. The available theoretical results indicate that the rate of functional optimal value growth with the growth of the investment horizon in the problem of optimal investment is equal to the reciprocal of the largest root of the investment function, which does not exceed one. This theoretical result suggests that the solutions to the primal and dual optimal investment problems satisfy the turnpike property. In this paper, examples are used to study the rate of convergence of the dual problem solution to the turnpike, depending on a set of roots of the investment polynomial.