THE FORMULATION AND SOLUTION OF SOME PROBLEMS OF THE THEORY OF INVESTMENT WITH OCCASIONAL PRIVATE BENEFITS
Y.D. Gelrud, O.V. Loginovskiy
The article discusses an alternative investment model with given probabilities of investment success and with a random distribution function of the benefits from them. A number of problems are formulated that most often arise when using this mathematical model. Submitted and solved the problem of finding the threshold for a given contract. As a result, it is shown that it is necessary to establish the value of the investment slightly higher than the threshold from which the entrepreneur evades the contract. It is shown that in exceptional cases, if an entrepreneur is indifferent between evasion and work, he decides to work. The task of finding the maximum amount of debt for a given investment threshold is investigated. It is assumed that the investor knows that if the volume is less than the investment threshold, then the entrepreneur works, and if the amount of debt is greater than the investment volume, then the entrepreneur evades, because the expected return on investment must be positive, and the investor must be insured to agree to the contract. The expected utility of an entrepreneur for a given investment threshold has been determined. The conditions were found under which the contract is optimal for an entrepreneur (subject to the break-even of investors). It is shown that in order to stimulate an entrepreneur to work, the “threshold remuneration” should be quite high (somewhere in the upper half of the expected profitability of the entrepreneur). The situation in which the private benefit is observable and verifiable is investigated. Solved the problem of determining the optimal contract between the entrepreneur and investors (compensation can be made depending on the level of private benefits). The proposed conditions for the adjustment of the contract with increasing benefits. It is shown that the optimal contract for an entrepreneur implies zero return for the investor. An analytical solution of these problems is given taking into account the stated requirements and limitations.
Keywords: : alternative investment model, entrepreneur’s expected utility, investment.