The potential of applying mathematical research methods in the field of household insurance

Foreign research in the field of insurance is carried out with the active use of special methods that allow empirically testing the hypothesis and modeling the expected result. Almost every job is performed using mathematical tools that allow you to build complex models, predict the behavior of potential policyholders and the situation in local insurance markets. This provides a practice-oriented result, enriches the theory of behavioral finance, allows us to explore multifactorial dependencies and form balanced insurance portfolios even for complexly organized systems.

Research focused on maximizing the utility of household consumption and savings deserves special attention. Insurance coverage is accepted as a mandatory element of financial planning. At the same time, it is included in the optimization plan as a way to compensate for unforeseen expenses and as an investment tool. Thus, in order to find the optimal life insurance strategy with a focus on determining the amount of insurance that maximizes the utility of household consumption, Erhan Bayraktar [1, p. 1-22] uses exclusively mathematical apparatus: it reduces the problem to solving variational inequality [1, p. 6], in which the main modeled components are household income, probability of death and consequently, the loss of this income, as well as the survivor's allowance. Further, in order to compare consumption rates in the options for paying a one-time insurance premium and making periodic payments based on the theory of ruin, the study continues, as the author himself notes, "inspired by actuarial mathematics" [1, p. 18]. Mathematical research methods have made it possible to determine the optimal amount of life insurance for households consisting of two employees focused on exponential utility, that is, excluding wealth as a factor in accessing life insurance.

Such tasks are multi-variable, most often they differ in the set of factors studied, the degree of detail of the "picture" of the household and the conditions in which it develops. They are united by the fact that solving such problems is impossible without the use of mathematical modeling and stress testing methods. As an example, we will cite the study by I. Vidangos [2], which raises the problem of household insurance savings with multiple sources of risk, that is, in fact, conditions close to the real situation are recreated. The author builds a consumption model at different stages of the life cycle, in which household income is subject to shocks related to personal risks (disability, health) and financial ones – employment, job change, lower wages and working hours [2]. The assessment of the importance of such diverse sources of risk for household well-being is based on the results of work with a system of equations focused on solving the problem of maximizing. The study itself is presented on 65 pages, 90 percent of which is occupied by mathematical calculations.

It is worth noting that the presented works are only an example of foreign studies in which mathematical and econometric research methods are actively used in relation to households and their insurance behavior. The abundance of such studies, among other things, can be judged by evaluating the citation lists. Each article is supported by a reference to a variety of widely presented works by other researchers who successfully combine insurance, mathematics, and econometrics. For example, in work I. Vidangos [2], presents 75 sources attesting to the use of mathematical and statistical apparatus by the authors. The results obtained make it possible to form a multidimensional portrait of a potential policyholder, taking into account his internal social ties and external dependencies, predict insurance behavior in any local insurance markets, and model the choice between insurance, consumption, and unorganized savings. Unfortunately, there are not many Russian-language articles on such topics yet, and research methods are rarely associated with mathematical calculations (the only exceptions are highly specialized material posted by actuaries). 

At the same time, Russian scientists are gradually expanding the field of insurance research and are beginning to pay closer attention to the opportunities offered by research methods that have not yet become "classical" for this field of knowledge. For example, applied econometrics is found in [3, p. 62-89], where a multidimensional probit model is built for households with children (note that the list of references here also mainly consists of foreign sources). However, this is most often a correlation and regression analysis conducted in relation to the insurance market as a whole [4, p. 430-435]. Thus, there is an obvious need for local research (especially in the field of behavioral finance) conducted using a variety of modern methods that allow modeling the choice of policyholders and beneficiaries, optimizing their budget and building optimal insurance portfolios.