What is stochastic modeling?
Stochastic modeling is a technique for presenting data or predicting results that takes into account a certain degree of randomness or unpredictability. The insurance industry, for example, relies heavily on stochastic modeling to predict the future condition of company balance sheets, as these may depend on unpredictable events that result in claims payments. Many other industries and fields of study can benefit from stochastic modeling, such as statistics, equity investing, biology, linguistics, and quantum physics.
Especially in the insurance world, stochastic modeling is crucial in determining which outcomes are to be expected versus which are unlikely. Instead of using fixed variables, as in other mathematical models, a stochastic model incorporates random variations to predict future conditions and see what they might look like. Of course, the possibility of random variation implies that many can occur. For this reason, stochastic models are not run just once, but hundreds or even thousands of times. This larger collection of data not only expresses which outcomes are more likely, but also what ranges to expect.
To understand the idea of stochastic modeling, it may be helpful to consider that it is somewhat the opposite of deterministic modeling. This second type of modeling is what most elementary mathematics consists of. The solution to a problem can usually only have one correct answer, and the graph of a function can only have a specific set of values. Stochastic modeling, on the other hand, is like varying a complicated mathematical problem a bit to see how the solution is affected, and then doing it many times and in different ways. These small variations represent the randomness or unpredictability of real-world events and their effects.
Another real application of stochastic modeling, besides insurance, is manufacturing. Manufacturing is considered a stochastic process due to the effect that unknown or random variables can have on the final result. For example, a factory that manufactures a certain product will always find that a small percentage of the products do not go as planned and cannot be sold. This may be due to several factors, such as the quality of the inputs, the working conditions of the production machinery, the competence of the employees, among others. The unpredictability of how these factors affect results can be modeled to predict a certain manufacturing error rate, which can be planned in advance.