Stochastic model in the economy. Deterministic and stochastic models

The stochastic model describes the situation when there is uncertainty. In other words, the process is characterized by a certain degree of randomness. The very adjective "stochastic" comes from the Greek word "guess". Since uncertainty is a key characteristic of everyday life, such a model can describe anything.

However, each time we apply it, we will get a different result. Therefore, deterministic models are often used . Although they are not as close as possible to the real state of things, they always give the same result and make it easier to understand the situation, simplifying it by introducing a set of mathematical equations.

Main features

The stochastic model always includes one or more random variables. It seeks to reflect the real life in all its manifestations. Unlike the deterministic model, the stochastic model has no purpose to simplify everything and reduce it to known quantities. Therefore, uncertainty is its key characteristic. Stochastic models are suitable for describing anything, but they all have the following common features:

• Any stochastic model reflects all aspects of the problem for which study is created.
• The outcome of each of the phenomena is uncertain. Therefore, the model includes probabilities. The accuracy of their calculation depends on the correctness of the overall results.
• These probabilities can be used to predict or describe the processes themselves.

Deterministic and stochastic models

For some, life is a series of random events, for others - the processes in which the cause causes the investigation. In fact, it is characterized by uncertainty, but not always and not in everything. Therefore, it is sometimes difficult to find clear differences between stochastic and deterministic models. Probabilities are a fairly subjective indicator.

For example, consider the situation with a coin toss. At first glance, it seems that the probability of a "tails" falling out is 50%. Therefore, it is necessary to use a deterministic model. However, in practice it turns out that much depends on the sleight of hand of the players and the perfection of balancing the coin. This means that you need to use a stochastic model. There are always parameters that we do not know. In real life, the cause always causes an effect, but there is also some degree of uncertainty. The choice between the use of deterministic and stochastic models depends on what we are willing to forgo - the simplicity of analysis or realism.

In the theory of chaos

Recently, the concept of which model is called stochastic has become even more diffuse. This is due to the development of the so-called theory of chaos. It describes deterministic models that can give different results with a slight change in the initial parameters. This is similar to the introduction to the calculation of uncertainty. Many scientists even admitted that this is already a stochastic model.

Lothar Breyer elegantly explained everything with the help of poetic images. He wrote: "A mountain stream, a beating heart, a smallpox epidemic, a column of rising smoke - all this is an example of a dynamic phenomenon, which, it seems, is sometimes characterized by chance. In reality, such processes are always subject to a certain order, which scientists and engineers are only beginning to understand. This is the so-called deterministic chaos. " The new theory sounds very plausible, so many modern scientists are its supporters. However, it still remains little developed, and it is quite difficult to apply it to statistical calculations. Therefore, stochastic or deterministic models are often used.

Building

The stochastic mathematical model begins with the choice of the space of elementary outcomes. So in statistics, a list of possible outcomes of the process or event is called. Then the researcher determines the probability of each of the elementary outcomes. Usually this is done on the basis of a certain methodology.

However, probabilities are still a fairly subjective parameter. Then the researcher determines what events are most interesting for solving the problem. After that, he simply determines their probability.

Example

Consider the process of constructing the simplest stochastic model. Suppose we roll a cube. If there is a "six" or "one", then our winnings will be ten dollars. The process of constructing a stochastic model in this case will look like this:

• We define the space of elementary outcomes. The cube has six faces, so one, two, three, four, five, and six can fall out.
• The probability of each of the outcomes will be 1/6, no matter how much we throw the cube.
• Now we need to determine the outcomes that interest us. This is a fall of the face with the figure "six" or "one".
• Finally, we can determine the probability of the event of interest to us. It is 1/3. We summarize the probabilities of both elementary events of interest to us: 1/6 + 1/6 = 2/6 = 1/3.

Concept and result

Stochastic modeling is often used in gambling. But it is indispensable in economic forecasting, as they allow deeper understanding of the situation than deterministic ones. Stochastic models in the economy are often used in making investment decisions. They allow you to make assumptions about the profitability of investments in certain assets or their groups.

Modeling makes financial planning more efficient. With its help, investors and traders optimize the distribution of their assets. The use of stochastic modeling always has advantages in the long run. In some industries, refusal or inability to use it can even lead to bankruptcy of the enterprise. This is due to the fact that in real life new important parameters appear daily, and if they are not taken into account, this can have catastrophic consequences.