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Optimization for Insurance Companies

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1. Challenges

The most critical challenges in the insurance industry are:

  1. Insurers set the price of their products without knowing production costs. This is one of the critical challenges that the insurance industry faces constantly. Most industries know the cost of resources – materials, labor, etc. and the profit margin to calculate the price of their products. However, on the contrary, insurance companies do not know the cost of an insurance product when initially sold. The cost of the actual insurance product may not be known for years until all the claims are paid (especially casualty products which can have a long claim tail). So, insurance companies (underwriters and actuaries) rely on historical data to predict future risk trends and determine premium rates to price their products accordingly.
  2. In the insurance industry, an important question arises: how can insurance renewal prices be adjusted? Such an adjustment has two conflicting objectives. On the one hand, insurers are forced to retain existing customers. On the other hand, insurers are also forced to increase revenue. Intuitively, one might assume that revenue increases by offering high renewal prices. However, this might also cause many customers to terminate their contracts. Contrarily, low renewal prices help retain most existing customers but could negatively affect revenue. Therefore, adjusting renewal prices is a non-trivial problem for the insurance industry.
  3. In many cases, existing rates are “rates in a table,” and no factor-based relationships among them are considered.
  4. It is challenging to manage rates and ensure consistency during rate changes. So, insurers should try to minimize rate disruption. Sometimes they use trial-and-error, which is highly time-consuming.
  5. The liability stream of insurance companies often stretches several years into the future. Therefore, there is always the need to determine a portfolio of bonds or other assets whose cash-flows replicate those of the liability stream. Insurance regulatory authorities require that insurance companies must demonstrate solvency. To achieve this, an insurance company needs to determine a fair market value of its liability by finding a replicating portfolio consisting of default-free bonds.
  6. Life insurance companies can be led to catastrophic situations if they do not pay more careful attention when deciding the premium charged to the policyholder and when carrying out the valuation of the options embedded in it. Furthermore, the inaccurate pricing of the policies and options represents a potential hazard for the company and ineffective management of the company’s assets and liability. As a result, these problems have drawn the attention of insurance companies, investors, and researchers.
  7. Traditional credibility models take into account the known history of a policyholder and project it into policy rate. However, for new clients coming for a new insurance policy, the history need not be known, or the information may be unreliable. Thus, traditional approaches of credibility theory are not efficient.
  8. Life insurance companies have become more innovative when designing their products to gain ground in a very competitive environment. Usually, these contracts embed different types of financial options, making the contract attractive not only for those who seek insurance but also for those who seek profitable investment opportunities. Minimum guarantee rate of return, reversionary bonus, right of surrender are some common features that we can find in life insurance contracts everywhere in the world. However, as much as these products have become innovative, they have also become more complex. Thus, the proper determination of the premium to be charged is a significant concern for life insurance companies.
  9. In the insurance industry, risk management decisions have important implications for solvency, earnings and tax management and directly impact the economic value of insurance firms. As a result, determining the optimal extent, type, and relative mix of reinsurance and retentions is a key strategic issue for internal stakeholders, such as policyholders and investors, and external stakeholders, such as reinsurance partners and credit rating agencies, fiscal authorities, and industry regulators.

2. How Optimization Can Help

The main optimization problems in the insurance industry are:

  • Portfolio risk management applications
  • Seeking optimal reinsurance structures
  • Managing catastrophe exposure
  • Optimization of tariffs
  • Optimization of insurance portfolios
  • Optimal management of the dividend policy

The main advantages of applying optimization approaches to the insurance industry are:

  • Increased profit margins
  • Increased volume of business (premiums)
  • Increased customer loyalty (higher retention rates on current business)
  • Higher conversion ratios (number of new policy offers accepted, divided by the number of applicants on new business) for desired classes
  • maximizing customer lifetime value & loyalty
  • Automating the decision-making process reduces many hours of guesswork per state/sub-line down to a few minutes.
  • Satisfying the business constraints such as limits on the volume of business to be written and limits on desired retention rate through optimization models
  • Eliminating premium reversals (Premium Reversal is the activity used to reverse the premium applied to the contract due to various reasons such as account closed, insufficient funds, stop payment or unauthorized payment.)
  • Considering retention/conversion effects and price elasticity
  • Assurance of the optimal solution.

Optimization can help insurers operate more efficiently and cost-effectively in the following ways:

1) Price optimization is the practice of charging higher rates based on the likelihood that a person will not shop around for a lower price with a different insurer. Price optimization helps insurers fine-tune the premium they will charge for a policy. Price optimization starts from traditionally calculated prices but mathematically considers “price elasticity of demand” also. We can develop price optimization models and algorithms based on all kinds of personal data, including loyalty to other service providers and shopping behavior, but not your driving habits.

Important Statistics: Insurance companies employ actuaries who use actual loss and expense data to estimate a range of reasonable rates. Within those boundaries, management determines the final rates that will be charged. Some insurers have begun to use sophisticated optimization models to help them ascertain appropriate pricing. According to a 2013 survey by Earnix, a software provider of price optimization products to the insurance industry, 63% of insurance companies either currently optimize their prices or plan to implement optimization in the near future; additionally, among companies with more than $1 billion in annual auto insurance premiums, 45% employ price optimization techniques.

We can consider various strategies in our price optimization models, including but not limited to:

  • Increasing profit margins by analyzing competitors’ prices
  • Obtaining and retaining business (strategies to boost new and renewal policy counts)
  • Managing claims (maximizing customer loyalty by adjusting premiums or the effect of accidents on premiums)

To implement a price optimization solution, we should consider the following essential components:

  • Predictive Modeling: We should use analytical tools to create what-if scenarios and impact analysis to predict future behavior and improve underwriting performance
  • Data Management: The quality of data, especially historic policy, customer and claims data combined with external big data availability is the key to using price optimization
  • Analytics Processing: We should develop dashboard tools that help insurers better understand and evaluate critical risk elements.
  • Competitive Landscape: Price optimization requires a thorough understanding of the competition, industry pricing strategies, customer data and customer buying preferences

Mathematical optimization is a very powerful analytical technology that, together with machine learning and advanced statistical models, brings great results by allowing insurers to run and simulate different scenarios, see how their KPIs are affected and ultimately select the best course of action. Therefore, we should develop our tools based on the following three pillars:

  • Predictive\Machine Learning modeling: We should enable the development and integration of various Predictive\Machine Learning models, focusing on making sure these models can be appropriately leveraged for pricing, rating & personalization strategies. With this goal in mind, we can develop a hybrid model that takes advantage of the predictive power of Machine Learning models and the causal inferencing of classical statistical models.
  • Optimization: We can include a broad set of optimization models or algorithms geared to handle different pricing & rating structures, regulatory & business requirements, and market scenarios. These models and algorithms support solving complex portfolios, lifetime value, multi-product, rank, and customer-centric optimization problems.
  • Smart automation: Our tools should enable smart automation of data, modeling, and pricing activities, including dynamic price tuning methodology, which allows organizations, where applicable, to make automatic pricing adjustments as needed.

2) We can develop rating factor optimization tools. To change the final price of the policy, insurers need to change several factor parameters. But the change in each factor influences more than one risk profile. Therefore, we can use an optimization tool to optimize the factor values directly rather than the final prices, as shown in the following figure. In addition to the insurer’s business constraints, we can consider other constraints such as monotonicity of rate factors, the maximum change from the current rate by each factor (e.g. not more than +/-2% relative to current value)

3) We can develop an optimization tool for renewal price adjustment. In particular, the renewal price adjustment problem is considered as follows: The insurer company has a portfolio of customers. Then, when it is time to renew the customer prices, the insurer takes the first client from the portfolio and decides which renewal price to offer him/her taking into account the current situation of the company (i.e., current revenue retention). Whether the customer accepts the renewal price or not, the insurer’s decision leads the company to a new situation (e.g., if the customer does not accept the renewal price, the insurance company will have one customer less and, hence, lower revenue). Additionally, we can know if the insurer’s decision has been good or bad (e.g., if the insurer’s decision increases the revenue, we can consider that the decision has been good and bad otherwise). Thus, one can take into account the utility of each particular decision. Then, given the new situation of the company, the insurer takes the next customer from the portfolio, makes a decision, and so on until the insurer makes a decision for each of the customers in the portfolio. In this way, the problem can be seen as a succession of situations (states), decisions (actions), and utilities (rewards). Therefore, we can model this problem as a Markov decision process. This modeling technique introduces two benefits: it takes into account the long-term effects of each decision and takes into account the expected value of each decision. Each particular customer’s decision should be optimized considering the sequential process involved and the optimization criteria selected (e.g., maximization of the revenue).

4) We can develop optimization tools based on catastrophe modeling, which is becoming increasingly important to insurance companies as they make decisions on catastrophe coverages, premiums, reinsurance agreements, and the effects of mitigation measures (Note: earthquakes, floods, tornados, etc. are considered as catastrophic events). For example, we can develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision-making on coverages of losses, profits, stability, and insurers’ survival.  It is possible to simulate catastrophes in a region and analyze the impact of different combinations of decision variables on the performance of insurance companies.  A catastrophe may affect different locations and produce rare and highly correlated losses in space and time. It may ruin many insurers if their risk exposures are not properly diversified among locations. The multidimensional distribution of claims from different locations depends on decision variables such as the insurer’s coverage at different locations, spatial and temporal characteristics of possible catastrophes, and insured values’ vulnerability.

5)  We can focus on the rating of non-life insurance contracts. Traditional credibility models take into account the known history of a policyholder and project it into the policy rate. However, for new clients coming for a new insurance policy, the history need not be known or the information may be unreliable. Thus, traditional approaches of credibility theory cannot be used. Therefore, we can employ models based on settled claims of new contracts from the previous years. This experience is transferred using generalized linear models, which cover many important regressions. Generalized linear models are used for pure premium estimation based on a priori characteristics of the insurance policy, insured object, and policyholder.

6) We can develop optimization tools that provide optimal life insurance participating policy by maximizing the policy’s profit. In this type of life insurance policy, a minimum interest is credited to policyholders, and additional interest may be credited according to the performance of a reference investment portfolio. Furthermore, policyholders can sell back the contract to the insurance company before maturity and receive a surrender value. For this purpose, we should first derive a formula to calculate the expected payments of the policy using the notion of fair valuation. Then, we should build an optimization model to decide the minimum guarantee, participating rate, and premium.

Definition: When the insured event is based upon the lives of the individuals mentioned in the contract, the policy is designated as a life insurance policy. Typically, these policies are divided into two major categories: protection policies and investment policies. The former is designed to provide a benefit (usually a lump sum payment) upon the insured’s death; in the latter, the main goal is to provide growth of capital.

7) We can develop stochastic optimization models that can be employed for insurance portfolio optimization in the presence of background risk. The optimal solutions of these models answer the question of whether the new risk is a good addition to the existing portfolio or not.

8) We can develop optimization models and algorithms that determine the optimal premium that should be charged to the policyholder to maximize the company’s profits on a specific type of policy to meet all the company’s contractual obligations due to the minimum guarantee rate and participation rate.

9) We can develop optimization models as a control problem with stochastic interest rates for designing optimal dividend plans, considering the following concerns. The bonus payments typically contribute significantly to the total benefits and thus constitute one of the most important decision problems in traditional life and pension insurance because it is up to the company to decide on the dividend/bonus plan. Two concerns are involved: On the one hand, the company is urged to hand out dividends to the insured regularly, partly to satisfy current customers and perhaps even try to gain shares in the competitive market of the insurance business, and partly by legislative demands. On the other hand, the companies must see to it that they do not hand out more than they can afford, that is, they should always be able to meet all future obligations. It should be noted that dividends and bonuses, which have been credited/paid out to a policy at one stage, cannot be reclaimed later on.

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