Международная студенческая научно-практическая конференция «Инновационное развитие государства: проблемы и перспективы глазам молодых ученых». Том 2

PhD Yakovenko O.G., Leont’yev V.Y., Goncharova Y.S.

Oles Honchar Dnipropetrovsk National University, Ukraine


One of the important sectors of the economy is real estate market. However, in Ukraine it is characterized by uneven development and imperfect legislative base. Unstable real estate market can make a negative impact on the economic reforms. It inhibits them. Unsettled real estate market is always a source of social tension in society, so that today the main problem in Ukraine – accommodation [1].

The real estate market is a complex, branched structure.

Real Estate market has the following functions:

- Effective solution of social problems related to the creation and use of valuable properties of real estate;

- Exclusion of full or partial ownership of real estate from one economic entity to another and protect their rights;

- Free pricing on objects and services;

- Redistribution of investment flows between competing types of property;

- Redistribution of investment flows between competing ways of land use.

Many participants of the real estate market perform different operations. The main of them are realtors. Consider some approaches to modeling realtor’s behavior with credit strategy optimization.

Let at any time (variable t is continuous) realtor can take a cash loan for total amount k(t) at a constant rate формула. This loan is used for home buying which worth is v(t). The main purpose of an estate agent is further sale of housing and obtaining a corresponding income. Quantity of goods that to be sold at time t is directly proportional to the valuev(t) with constant coefficient α, and quantity of goods in time t+Δt, where Δt> 0 – arbitrary increment of time is increased by the value of loan at time t the difference between the number of goods at time t and the size of its implementation, that is формула. The last assumption allows modeling the balanced equation of the dynamics of an existing product in financial form:

 формула (1)

Differential equation should be supplemented by the initial condition:

 формула (2)

This condition means that at the initial time t0=0 the realtor has initial inventory value of v0 currency. Since the loan amount is always limited value, the previous relations need to connect the restrictions on credit:

 формула (3)

where β – upper limit of the credit loan.

Now the purpose of the commercial agent is formalized. His income is determined by the difference between income from the sale of goods and payment of interest. Assuming that the revenue from each unit of sold goods is γ per cent, and the activity of the agent studied in the time interval [0, T], (where T – fixed time) then set the problem to determine the optimal loan k(t) which would maximize total income. In other words, in a formalized form this problem is equivalent to next problem [2]:

 формула. (4)

Previous relations describing the problem of optimal control of Lagrangian functional and free right end of the phase trajectory v(t). Guidance of this problem is the functionk(t). To analysis the problem we need to use Pontryagin maximum principle.

The proposed dynamic model of optimal realtor’s behavior shows one of the possible approaches to modeling one of the links in the real estate market.


1. Романюк Е. Рынок недвижимости / Е. Романюк // Бизнес. – 2007. – №35. – С.116-121.

2. Григорків, В. Моделювання оптимальної кредитної стратегії ріелтора / В. Григорків, О. Ярошенко // Економічна кібернетика. – 2007. – № 1-2 (43-44). – С. 4-9.