Behavioral models in insurance risk management

Behavioral characteristics attributed to consumers of insurance services are a relevant factor for analyzing the current situation in the insurance market and developing effective strategies for insurers’ actions. In turn, considering these characteristics allows the insurer to be more successful in the highly competitive field, achieving mutual satisfaction in interacting with the customer. This study is aimed to develop cognitive models of the situation (frame) “Insurance”, taking into account the specifics of the Russian insurance market and systemic factors affecting participants’ behavior in the market. In this regard, the study involves systemizing risks at various levels of the economic system, generalizing factors for the motivation of insurance consumers, developing descriptive and economic-mathematical models for the behavior of economic entities in risky situations.The results obtained represent a behavioral model of interactions among insurance market entities, which determines opportunities for efficient and mutually beneficial coordination of their activities. The developed model includes the following elements: structured individual and institutional frames “Insurance”; a professional index of interest in insurance presented in the form of a mathematical model; methodology for governing the relationships among insurance participants in the digital environment.The recommendations enable predictions of the situation in the insurance market and allow most accurately defining the consumer needs in the conditions of market changes.


INTRODUCTION
From the perspective of the interdisciplinary approach, insurance can be referred to as complex socio-economic phenomena whose alterations are caused by situational factors of various levels -trends in the world markets, the Covid-19 pandemic, internal policy, local taxes, etc. Therefore, the application of cognitive models in a situational analysis is relevant for the decision-making process performed by insurance market participants.
Actually, the problem under study insists on the lack of an optimal interaction between the insurer and the policyholder that would be useful and effective for both parties. The purpose of this paper is to consider the creation of a cognitive model for analyzing the situation of "Insurance" that could take into account various parameters of the specific state of affairs in the insurance industry, provide an opportunity for digital processing of available information, and offer options for the probabilistic development of the situation.
In the meantime, modeling of the construct (the frame "Insurance") is certain to be effective in analytical practices and be feasible in meth-ods of processing big data. The paper proposes a new approach to tackling the problem of effective interactions among insurance market participants, integrating the economic and psychological features of human cooperation in contemporary market conditions. The application of the frame allows determining the behavioral model of market participants, primarily consumers, analyzing and predicting their actions in the insurance market segment (motivation in making decisions about purchasing a product, changes in the consumption volume, etc.).
Since the problems considered belong to the multidisciplinary scientific discourse, there have been a few scientific papers devoted to this topic. That is why research involving data and methods from different scientific areas is of great interest for exploring the issue. Thus, the paper is based on the theory of frames and the stereotypical models of human behavior based on it. These questions have been studied by scientists in the field of sociology (Bruner, 1993;Hayek, 2001;Weise, 1993;Lindenberg, 1985), psychology (Pyastolov & Zadorozhnyuk, 2003;Kahneman & Tversky, 2003;Simon, 1995;Hoffman, 2003), cybernetics (Minsky, 1979), and cognitive semantics (Fillmore, 1988;Boldyrev, 2016). To examine the human motivation in the economic and financial decision-making process, the scientific works reputed to be classical in the field of economic theory are applied in the paper (Smith, 2009;Eggertson, 2001;Schumpeter, 1989;Heine, 1997); they describe, first of all, traditional rational models of human behavior. Current studies in the field of behavioral and situational economics are of considerable interest in the information society (Avtonomov & Belyanin, 2011;Kapelyushnikov, 2013;Becker, 2003;Hands, 2012;Simon, 1957;Camerer et al., 2003). Most economic entities are not inclined to make rational decisions in risky situations and are guided by other motives (personal experience, recommendations of other people, information obtained from the Internet, influences of marketers, and advertising). Behavioral actions of economic entities are considered using the insurance industry as an example. For this purpose publications on risk theory and risk management have been used (

Framing of homo economicus activity
It should be pointed out that contemporary investigative practices characterized by synthesizing approaches are methodologically typical for various scientific disciplines. Thus, the research object can be explored taking into account its various aspects and drawing complex conclusions.
In this regard, particular economic realia can be studied more substantially, considering the socio-cultural environment that is reflected in the cognitive models of its representatives. Insurance in turn should be attributed to multifaceted socioeconomic phenomena that can be investigated from the perspective of the interdisciplinary approach.
In this paper, insurance is proposed to consider as a frame. The concept "frame" came to promi-nence due to the works of Hoffman (2003), being viewed in a psychological and sociological domain. Frames are presented as situations based on the rules governing events and aimed at organizing and involving participants in the events (Hoffman, 2003). Frames as cognitive products are segmenting social reality. They are treated as forms of structuring life experience and communication. The interpretation of frames serves for explaining and predicting the behavior of people. Frames have become an investigation object within examining the problems of artificial intellect and linguistic studies (Minsky, 1979;Fillmore, 1988). In this study, a frame is understood as a cognitive model structuring the individual experience of a man and conveying knowledge and opinions about a certain, often repeated situation (Boldyrev, 2016).
Behavioral models are important in the economic life of citizens, as they validate decision-making in the field of lending, investment, insurance, and other financial transactions that ultimately affect the level and quality of citizens' life.
In fact, the socio-psychological features of people's behavior are formed under the influence of various factors intrinsic to the external and internal environment. It makes sense to apply these features in different spheres of economic life to understand the motivation of consumers and other market participants to stimulate demand for certain types of services and develop definite segments of the financial market.
An important concept of the insurance industry is trust. For loyal customers, trust and commitment take priority over satisfaction, being mediators that balance a complex attitude to the product and future intentions (Garbarino & Johnson, 1999).
Conventional insurance theory is based on the tenets of neoclassical economic theory. However, it does not explain some phenomena of real insurance markets. In particular, these include perception of insurance according to the theory of utility, peculiarities of people's attitude to low-probability events, underestimating consequences of high-probability events, choice of inadequate insurance coverage.
Explicating these phenomena necessitates elaborating a behavioral insurance theory based on the theory of behavioral finance that in turn is derived from behavioral economics. There is a need for altering the paradigms of the conventional theory of insurance, which assume absolutely rational behavior appropriate to an individual, perfect composure (self-control), and egoism (Khominich et al., 2012).
It should be emphasized that the entire behavioral potential of insurance entities is associated with the peculiarities of the risk management and the choice of insurance products when interacting cognitive and emotional aspects in decision-making conditions. Thus, the influence of the emotional behavioral reaction can lead not only to the expected favorable but also to undesirable beha vioral consequences and decisions that are far from optimal ones. In this case, a way of processing information and a person's perception of risk in the decision-making process become relevant factors.
People generally demonstrate irrational behavior in situations associated with uncertainty and risk. For instance, when deciding to insure themselves, they prefer low deductibles. Such decisions are based on the misconception that the lower is the deductible, the higher is the probability that the insurance company will pay in exchange for the premiums paid. At the same time, insurance is considered a form of investment. A higher premium associated with a lower deductible represents higher costs for forming the load in the structure of the insurance premium. That is caused by high administrative costs for processing indemnity insurance claims. Accordingly, an individual overpays by purchasing an insurance policy to provide protection against losses that are very insignificant and which could be quite easily compensated by the individual (Lomovtseva & Trofimova, 2015).
Individuals frequently prefer not to be insured against low-probability events having potentially high amounts of losses (natural disasters, floods, fires, etc.). Most people ignore low-probability events because they avoid thinking about possible negative consequences and act up to the principle "This will not happen to me!". Finally, the decision on high-risk insurance is highly likely to be made after a loss occurs then before that. A risky event may become more significant in people's consciousness due to misconceptions about the possibility of its reoccurrence. People worry more about the risk event and therefore they aim at investing in protection.

Behavioral characteristics of economic entities in risk situations
Investigating the behavior of economic entities in various situations having a risky nature is of particular importance in contemporary society. Models of risk behavior in the economy have been widely examined. Thus, Thaler (2017) studies the psychological aspects defining buyer's activity, and difficulties faced while making a decision on purchasing goods and services. Shaboltas (2014) considers comprehensively the category of risk and models of human risk behavior from the psychologist's point of view. Pantin et al. (2018) scrutinize the types of risks inherent in the Russian economy and methods of managing them. The risk category, types of socioeconomic risks, and techniques of risk management are discussed by Istomina and Fedorova (2018). Behavioral models of choice in risky situations on the example of objects of investment in securities papers and other financial assets are researched by Danthine and Donaldson (2015). Kenneth (1998) considers the framework as a complex method to be used by any subject to determine a strategy for managing a risky situation. Many scientists note a close relationship between risks and insurance (Rejda & McNamara, 2014).
Behavioral models in risky situations are of great significance in modern socioeconomic systems, since negative catastrophic events regularly take place in them both at the local and global levels.
In this regard, to preserve the stability of the economic system, it is important to develop behavior principles for subjects who find themselves in a particular situation and to create methods for managing risky events aimed at eliminating or smoothing out negative consequences for individual subjects as well as states. The most significant risks inherent in each level of management in the socio-economic system are shown in Table 1.
Experts identify economic, environmental, geopolitical, social, and technological risks as global risks (Ivanov, 2017). The most significant risks given the possibility to manage are global events of an economic, social, and environmental character. However, all types of risks, one way or another, entail negative economic consequences. Thus, the latest global event of a non-economic nature -the Covid-19 pandemic -has had a large-scale impact on the entire world economy and social sphere.
The influence of risk factors on economic entities manifests itself in different ways, depending on the status of the entities. Therefore, they should be divided into three groups according to the levels of risk management: individuals, organizations, and the state.
As a consequence of risk situations, these subjects reveal themselves variously according to their status, as well as the personal characteristics of specific people making managerial decisions.

The level of the socioeconomic system
The main risks of a medium-term and long-term character Implementation risks and medium-sized businesses low investment attractiveness lack of investment potential and reduced competitiveness of the economy aging of production assets reduction in the production potential volatility of the national currency instability of the financial system Local . Their application is conditioned by the financial, organizational, and professional capabilities of the subjects involved in a risky situation. The main methods of risk management are shown schematically in Table 2.
The most universal method of risk management is the insurance method, since it allows protecting various entities against risks with minimal expenses, as well as acquiring knowledge and skills in this area.

Factors of demand for insurance services
Actually, a few studies have discussed the factors of demand for insurance services in Russian and foreign insurance science. In this regard, the investigations of Khitrova (2012) The reasons and factors for purchasing insurance services and refusing them have been researched by the rating agency Expert-RA (2021). Customers consider the intention of protecting their property and the obligation to purchase certain types of insurance as the main motives for acquiring insurance services.
The major causes of refusing to buy insurance services are as follows: 1) a lack of property requiring insurance protection; 2) a lack of financial opportunities to purchase an insurance policy; 3) a lack of economic benefits of buying an insurance policy; 5) negative reviews about insurers and poor quality of service.
In the process of choosing an insurer, the following behavioral models are the most common: 1) searching and comparing the proposed conditions that result in a rational model of choosing one of the available offers; 2) focusing on the recommendations of friends and acquaintances; 3) contacting the company to have dealt with earlier and to have provided an insurance product.
When choosing an insurance company, the priority criteria for policyholders are its reliability, cost of services, recommendations, and promptness of payments. Thus, the behavioral model of policyholders in purchasing or refusing insurance services and choosing a suitable insurance company is determined by the factors affecting the demand for insurance services, which can be divided into two groups (Figure 1).
Objective factors affect the insurance market equally, so they determine insurance expediency, as well as the economic opportunities of both insurers and policyholders. Only state authorities and the financial market regulator can influence the effect of these factors. Individual entities of the insurance market cannot exert an impact on objective factors, but they should take them into account in their activities as an element of risk.
In this regard, the combination of various factors affects the motivation of consumers to purchase insurance services. The most relevant factors within this study are the subjective factors of demand for insurance services since their investigation allows to realize fundamentally the behavioral model intrinsic to certain groups of policyholders (representatives of policyholders) classified according to definite characteristics.
Both insurers, competently building an insurance strategy in today's conditions of digitalization and improving the financial literacy of policyholders, and the state represented by the regulator can define subjective factors. For example, creating an insurance culture is a national task, but the factor is subjective, as people aim at copying mass behavior, in this case, they acquire insurance policies if other people are actively involved in it.

Behavioral models of economic entities in risky situations
Summarizing the theoretical research, two models of interacting economic entities in situations of uncertainty have been derived.
From the consumers' motivation viewpoint, relationships arising between the participants of economic affairs are considered from the perspective of the resource approach in combination with the "attitudinal" approach. The resource approach examines the dynamics and movement of resources between the participants of relations, and the "attitudinal" approach focuses on the position that any relationship contributes to the emerging of "attitudinal rent" applicable in all sectors of the economy.
In this respect, it is of great interest to research such interactions from the perspective of their development dynamics, taking into account a variety of objects united by a territory demonstrating stable internal relationships. The peculiarity of any interaction is a voluntary membership, therefore the number of participants is a variable value, which allows avoiding rigid determination of the functions of associations' participants. In turn, the definite approaches to governing customers' motivation can be distinguished (Table 3).
Thus, by applying a combination of the approaches, it is possible to achieve an increase in the efficiency of social interaction and motivation of consumers both in the field of using insurance mechanisms and in other sectors of the economy.
Situational behavior of economic entities involved in occurring a risk event with the participation of an insurance institution can be presented in Figure 2.
It is of great importance at each level of management to model typical risk situations significant for most subjects of economic relations, identify possible consequences and develop management decisions aimed at strengthening positive consequences and results and eliminating or reducing negative ones.
However, the main conclusion following the model is that insurance mechanisms should work effectively on the basis of supply and demand. Thus, in Russia, insurance mechanisms are not effective primarily because policyholders are extremely unwilling to purchase insurance services, and the actions of insurers' representatives are not always professional and aimed at satisfying the interests of the consumer.
In this regard, to comprehend the content of this problem and its causes, it is significant to start by researching consumer motivation to be implemented in demand indicators.

Demand analysis in the insurance services market
Insurance is the most important branch of the financial market since the lack of an effective insur-ance system or its unstable functioning hinders economic growth in the state (Pradhan & Dave, 2018). The insurance economy is becoming one of the central issues concerning economic development in modern nations. It not only illustrates new theories in practice but also has a heuristic effect when generating important macroeconomic ideas (Louberge, 1998).
At the same time, the decision-making process in the insurance sector undoubtedly has its specifics to be the object of various researches (  different trends in the development of insurance markets and the demand factors for insurance services in the world practice has revealed that the motives encouraging policyholders to purchase insurance policies or refuse them may differ according to countries and regions of the world. An important condition is a cultural and social environment in which the level of financial literacy of the population in the field of insurance is being raised.
In this connection, the factors of consumer motivation could be considered on the example of insurance services in Russia as a country having a complex territorial and national structure, as well as specific natural, climatic, and socioeconomic conditions.
Over the past few decades, there has been a problem of unstable demand for insurance services in Russia. The demand is differentiated depending on the form and type of insurance, as well as intra-country location (belonging to the subject of the Russian Federation). These aspects are expressed in the following: the amount of voluntary insurance varies significantly according to the general economic situation, which provokes instability of the insurance market. Figure 3 shows the dynamics of insurance premiums in Russia in conformity with the type of insurance.
The chart illustrates that the main market segments are life insurance, personal accident insurance, and medical insurance, as well as property insurance. These voluntary insurance services exactly correspond to the main directions from the perspective of stimulating sustainable demand influenced by market conditions.
Depending on the subject of the Russian Federation, the structure of insurance premiums differs both in sectors (personal insurance, property insurance, liability insurance) and forms (compulsory and voluntary). The regional structure of insurance premiums is shown in Figure 4. Figure 3 demonstrates the differences in the demand for insurance services in various territories of the country. This inequality is determined by dissimilarities in the standard of living in the regions, financial literacy of the population, ethnic and socioeconomic, as well as psychological factors.
In this regard, the professional index of insurance interest in dynamics was calculated in order to scrutinize the demand for insurance services. The index is based on the methodology proposed by Khominich et al. (2012). The model was modified in a definite way. Namely, some indicators based on statistical data were included in the calculation instead of initial indicators obtained by observation.
The construction of the index is presented in the form of the mathematical model consisting of  Multipliers are the weights of variables showing their significance according to the data of the sociological survey.
The dynamics of the professional index of insurance interest is presented in Figure 5.
Thus, the graph reveals an increase in voluntary insurance interest in 2015. In subsequent years there was a decline in the index, and in 2020 there was a slight trend of increasing demand for insurance services.
In order to effectively develop the insurance market involving the formation of a stable customer base, it is important to realize the motivation of potential and real insurance consumers in acquiring or rejecting the services. This information is relevant for the following categories of insurance subjects: insurance companies, regulatory authorities, and consumers of insurance services. Comprehensive investigating of socio-psychological motives typical for insurance consumers will enable regulating the insurance market on a national scale, taking into account the specifics of the regions.
A substantial element of the effective interaction between the insurer and the policyholder is market segmentation. When segmenting consumers, the insurer should consider both objective and subjective factors.
The target audience of insurance consumers schematically can be divided into three groups. Table  4 shows the complex characteristics intrinsic to different types of customers, given both objective and psychological factors.  Thus, the effective customer meets the main characteristics of a rational person. This type is a successful middle-aged person having a family who is interested in protecting against property and non-property risks. However, such a customer may or may not have a motivation for insurance. The second option is quite understandable in the conditions of an undeveloped insurance market, for example, the Russian market. If there is no motivation for insurance, the customer will use self-insurance methods.
The average customer represents the majority of policyholders. This group includes people with an average income level having different family and property statuses, as well as psychological char-acteristics. However, it is this segment that represents the main demand for mass insurance types, therefore it requires a smaller segmentation depending on the insurance types. Nevertheless, this category of customers may also have motivation, but may not.
The inefficient customer generally is undesirable in the sphere of insurance, since the person worsens the quality of the insurance portfolio. Such a customer makes decisions spontaneously, is influenced by the majority or advertising, does not understand the need for insurance, and often does not have the necessary income for this. The customer usually acquires insurance services as accompanying the purchase of other goods and services.   It should be highlighted that the given model of segmentation is approximate and can be improved taking into account the activity specifics inherent to a particular insurer. Modern technologies in insurance based on the use of neural networks also allow detailing this model.

DISCUSSION
The balanced development of the modern economy definitely requires exploring consumer motivation. This is especially relevant in such complex financial products as insurance services.
The study of modern behavioral theories and the possibility of their usage for researching the situational behavior of insurance entities in risky situations has been carried out in the paper.
It should be emphasized, to make a reasonable choice of an insurer and a service, the individual policyholder (a representative of the policyholder -a legal entity) needs knowledge of the basics of financial science and risk theory, as well as the use of rational thinking. This is especially essential when using digital sales channels that require independent and informed decisions. However, modern consumers are not always able to make economically competent decisions; they are often guided by the established experience, stereotypes, and recommendations of others.
In fact, two types of frames should be distinguished: individual and institutional. In the first case, it implies structuring the personal experience of an individual (a potential policyholder), the institutional framework is formulated by the insurer and aims at tactical/strategic strengthening and developing of the organization. Being a source of business activity, the insurance organization seeks to establish a connection, optimize the mutually beneficial relations by regulating the structures of the individual and institutional framework.
It should be noted that the study contains a synthesis of methods and approaches for investigating the behavioral aspects of economic entities. These techniques are offered by various sciences, such as psychology, linguistics, sociology, economic theory, financial theory, and insurance theory. This enables the development of a comprehensive model including both descriptive and economic approaches to examining the behavior and motivation of insurance market participants, primarily policyholders.
Therefore, the advantages of the proposed model are its originality, a systematic approach, as well as the versatility of use. It is suitable for governing risks not only in the insurance sector but also in the risk management system of an enterprise or a certain territory (region). However, the model needs to be improved by integrating it with modern digital algorithms and platforms in the insurance sphere. This is a perspective for future research in this direction.

CONCLUSION
In the conditions of increasing competition, insurers, on the one hand, aim at enhancing the quality of the insurance portfolio by attracting effective customers; on the other hand, they should offer different kinds of services to satisfy the customer.
The behavioral model proposed for economic entities in a risk situation makes it possible to analyze decision-making by both citizens and institutions, including policyholders, insurers, and the state.
Based on the study of the factors determining the demand for insurance services, the customer segmentation has been carried out that takes into account the objective and subjective characteristics of the customers and allows developing insurance services according to the demands of specific customer categories.
The proposed methods and models can be most effectively implemented in the conditions of digitalization of the economy. Thus, the usage of online sales channels for insurance services allows avoiding the