How Fear of High Premiums Makes Us Silent Insurance Strategists

Imagine this: you've scratched your bumper in a parking lot. The damage is three hundred euros. You know insurance covers it. But you also know: file a claim, and next year your premium jumps by five hundred. What do you do? You stay silent. You pay out of pocket. And this isn't an accident – it's a strategy. A strategy millions apply daily, often without even realizing they are part of a complex psychological and economic game.

A recent 2023 study for the first time connected two crucial pieces of this puzzle: the behavior of people who intentionally keep quiet about insurance events, and the reaction of insurance companies competing for these very clients. We're talking about a market operating on the «Bonus-Malus» system – the very one that rewards you with a discount for accident-free driving and punishes you with a premium hike for every scratch you decide to report.

When Silence is More Profitable Than Claiming Insurance

A Theater of One Decision: When Silence Is Worth More Than Words

Let's start with a simple question: why don't we report losses at all? The answer seems obvious – to avoid paying more later. But behind this «obvious» answer lies a whole world of calculations our brain performs automatically, even if we're not mathematicians.

When you face the choice – to file a claim or stay silent – you weigh two scenarios. First: get compensation today but pay a higher premium tomorrow. Second: pay now out of your own pocket but keep the low premium for the future. Researchers call this the «optimal claiming threshold». Sounds dry, but in reality, it's simply the amount below which you are willing to keep your mouth shut.

Suppose the difference between your current premium (Class A, «good driver») and the future one (Class B, «problem client») is five hundred euros a year. If the damage is two hundred euros, you stay silent: losing three hundred net makes no sense. If it's a thousand – you file a claim: the savings are obvious. But where is the line drawn? And most importantly – do insurance companies realize we are playing this game?

What Insurance Companies Know About Your Hidden Claims

The Double Bottom: What Insurers See

Insurance companies aren't stupid. They know we stay silent about small scratches. Moreover, they factor this into their calculations. But here's what's interesting: in a market where two (or more) companies compete, this game becomes three-sided. You choose what to keep quiet about. The company chooses what premium to set. And its competitor tries to lure you away by offering slightly better terms.

The model developed in this study described for the first time how these three players interact. Imagine a chess match where every move by one player changes the layout for the other two. An insurer lowers the Class A premium – you are more willing to stay «clean», silently paying for minor damages. A competitor raises the Class B premium – your silence threshold rises because moving to the «bad» class becomes even scarier.

Researchers proved: there is an equilibrium point in this game. A combination of premiums where no company wants to change the price (or they'll lose clients), and clients choose the optimal silence strategy. This is the Nash equilibrium – a concept from game theory describing a situation where it's unprofitable for anyone to deviate from their strategy if others don't change theirs.

Factors Defining Your Insurance Claim Threshold

The Anatomy of Silence: What Our Threshold Is Made Of

What determines how high your personal silence threshold will be? Researchers identified several key factors, and each of them is a window into our psychology.

The Premium Gap: The Price of a Mistake

The wider the gap between the «good» and «bad» class premiums, the larger the sum you are ready to swallow silently. If moving from Class A to Class B costs you an extra thousand euros a year, you'll easily pay out of pocket for damage worth four hundred or even six hundred euros. This isn't irrational – it's pure arithmetic of fear regarding future expenses.

The Discount Factor: How We Value Tomorrow

Remember the old saying: «A bird in the hand is worth two in the bush»? Economists call this future discounting. We tend to value today's money more than tomorrow's. If you're someone who lives in the «here and now», a high premium a year from now doesn't scare you – and your silence threshold will be lower. You'd rather file a claim, get compensation today, and worry about the future later. But if you tend to plan ahead and fear long-term costs – your threshold will skyrocket. You'll stay silent even about serious losses, just to avoid ending up in the «bad» class.

Accident Frequency: A Game of Probabilities

If you know (or suspect) that you have a high risk of accidents – say, you drive complex routes or often park in tight yards – your strategy changes. A high probability of new incidents makes the move to Class B almost inevitable. Why stay silent about the current damage then? You already realize: sooner or later you'll end up in the «penalty» class. Better to at least get compensation now.

Researchers modeled this situation using the Poisson distribution for accident frequency – a mathematical tool describing rare random events. And it turned out: the higher the accident frequency, the lower the silence threshold. The logic is simple: if an accident happens again tomorrow, there's no point in saving on today's.

How Competition Affects Insurance Claims and Premiums

Competition as a Catalyst: What Happens When There Are Two Companies

Now let's add a second player to the equation – a competing insurance company. What changes? Everything.

In a monopoly world, an insurer could dictate terms: here is the Class A premium, here is Class B, if you don't like it – walk. But when there are two companies on the market, they are forced to look over their shoulders at each other. If Company I sets the Class A premium too high, clients will leave for Company II. If Company II lowers the Class B premium too much, it will attract «problem» clients but might go into the red on costs.

The study showed: in this situation, premiums tend toward a point where they cover the insurer's expected costs but aren't high enough to scare off clients. Sounds like textbook capitalism, but the devil is in the details. Expected costs depend on how many losses clients stay silent about. And that, in turn, depends on the difference in premiums. The circle has closed.

The model described this vicious circle through a system of equations. The Class A premium must cover costs for large loss payouts (small ones are hidden by clients) plus account for the probability that the client stays in this class or moves to Class B. Similarly for Class B. These equations aren't an abstraction. They describe real decisions insurance actuaries make every day, even if not always formulating them so explicitly.

Numerical Analysis of Insurance Strategies

Numbers Don't Lie: What Numerical Analysis Showed

Theory is good, but what happens in reality? Researchers ran their model through a series of numerical experiments, varying parameters: accident frequency, average damage size, discount factor. And here is what they found.

Scenario 1: Accident Frequency Rises

Suppose the number of minor road accidents in a region has increased – say, due to bad roads or a rise in the number of cars. How will premiums react? They will rise for both classes. This is expected: more accidents – more payouts – higher premiums. But here's what's more interesting: the difference between Class A and Class B premiums will also increase. Why? Because insurers know: Class B clients get into accidents more often (according to their claim statistics), and the risk of new payouts for them is higher.

Scenario 2: Average Damage Size Decreases

Let's assume most accidents have become «minor» – scratches, dents, no more than a thousand euros at a time. How will this affect the market? Premiums will drop. Logical: lower average payout check – lower risk for the company. But the clients' silence threshold will hardly change. Why? Because it is determined not by the absolute size of the damage, but by the difference in premiums. If this difference remains the same, you will stay silent about the same amounts as before – only now they constitute a larger share of the average damage.

Scenario 3: Clients Become «Farsighted»

Imagine people suddenly started valuing the future more – say, due to an economic crisis that taught them to plan ahead. The discount factor rises: tomorrow's expenses are almost as frightening as today's. What will happen? Silence thresholds will skyrocket. Clients will stay silent even about large losses just to avoid moving to Class B. And insurance companies? They will lower premiums. Why? Because clients file fewer claims, company costs drop – and competition forces them to share this saving with the market.

The Hidden Economy of Unreported Insurance Claims

The Invisible Economy of the Unspoken

What does all this mean for us, ordinary people who just want to insure a car and not think about game theory?

First, it explains why insurance premiums sometimes seem illogical. You drove for a year without accidents, but the premium didn't drop – or even rose. Why? Perhaps because other clients started keeping quiet about minor losses more often, and the company recalculated its risks. Or a competitor left the market – and your company allowed itself to raise prices, knowing you have nowhere to go.

Second, it shows how our personal decisions add up to collective behavior that changes the entire market. When millions of drivers decide to keep quiet about a three-hundred-euro scratch, insurance companies see a drop in claim numbers. They interpret this as a reduction in risk – and might lower premiums. But this is an illusion. The risk hasn't dropped. We just learned to keep quiet. And this illusion is part of the equilibrium in which we all live.

Third, it reminds us: behind every price we see on the market stands an invisible game of expectations, calculations, and strategies. An insurance premium isn't just the «price of risk». It's the price of how we react to that price. The higher the Class B premium – the more we stay silent about minor losses. The more we stay silent – the lower the insurer estimates its costs. The lower the costs – the lower the premiums can be under competition. But if premiums drop, our silence threshold also drops – and the circle starts anew.

Future Questions About Insurance Claim Behavior

What's Next: Questions Without Answers

The study opened a door, but behind it lies much uncharted territory. The model considers two classes: «good» and «bad». But in reality, «Bonus-Malus» systems can have five, ten, fifteen levels. How does this complicate the game? Do clients develop new strategies – say, intentionally «skipping» through an intermediate class by filing one claim but staying silent about subsequent ones?

And another thing: the model assumes all clients are identical in risk level. But that's not true. Someone is genuinely a careful driver, and someone gets into accidents more often. Insurers try to account for this, but information is asymmetric: you know how careful you are, but they don't. How does this change the equilibrium? Can a careful driver «signal» their reliability by choosing a specific claim-filing strategy?

And finally: what if there are not two companies, but ten? Or a hundred? Competition intensifies, premiums fall – but does the equilibrium remain stable? Or does a moment come when companies start dumping prices, go into losses, and leave the market – and everything collapses back to an oligopoly?

Human Psychology and Insurance Decisions: A Deeper Look

The Psychology of Money in the Insurance Mirror

This story isn't just about insurance. It's a story about how we make decisions under uncertainty, when today's savings promise tomorrow's expenses, and tomorrow's expenses are foggy and abstract. Our brain handles such tasks poorly. We tend to overestimate the immediate and underestimate the distant. But when real money is at stake, we suddenly become intuitive strategists.

Think about it: we solve tasks daily that are mathematically equivalent to optimizing threshold strategies in a competitive equilibrium. We just don't call it that. We say: «I won't claim the three hundred euros, it's not worth it». But behind this lies a complex calculation our brain performs automatically, weighing probabilities, discounting the future, assessing risks.

And insurance companies play on the same strings. They know: we are afraid of losing status. Class A isn't just a low premium. It's a marker of a «good driver», a «responsible person». Moving to Class B is a humiliation, an admission of failure. And this fear works more powerfully than any numbers on a calculator.

That is why the «Bonus-Malus» system isn't just a pricing mechanism. It's a tool for behavior management. It turns us into accomplices in our own insurance. We decide what to keep quiet about and what to speak of. We regulate our own costs, choosing which losses are «worthy» of a claim. And in this process, we form that very invisible economy of the unspoken which defines prices for everyone else.

Money exists because we believe in it. But insurance premiums exist because we are afraid to lose them. And this difference – between belief and fear – is perhaps the key to understanding why the economy doesn't always behave as textbooks predict. Because behind every model stand living people who are simply trying not to overpay for a scratch on a bumper.