Analysis of mechanisms of production investment stimulation in an imperfect capital market based on a mathematical model

The problem of renewed market investment in the Russian real economy is closely related to the business environment state in the imperfect capital market in Russia and to the assessment of the profitability of investment projects. Difficulties in determining profitability in an imperfect monetary and credit system are associated with the significant discrepancy between the interest rates on deposits and loans and can be overcome by applying the Cantor–Lippman approach, which makes it possible to calculate the profitability of a pool of investment projects available to an investor. From the point of view of a production owner, market investment depends on the state of the business environment and competes with investment in consumption. The problem arises of estimating the profitability threshold at which private market investment is preferred to private consumption. We propose an approach to the solution of this problem in terms of a mathematical model of investment behavior of a production owner in an imperfect capital market. The model is formalized as an infinite-horizon optimal control problem with a state constraint. The solution of the problem is based on constructing a viscosity solution of the Hamilton–Jacobi–Bellman equation. It is shown that the investment strategy of a production owner can depend substantially on the business environment state. Based on the results of this study, an explanation is proposed for the transition from recovery growth to stagnation in the Russian economy in late 2007, which was accompanied by recession of investment activities in the manufacturing sector.