By refining and adapting a model originally developed for the agricultural risk insurance market (Duncan & Myers 2000), the research accurately reflects the dynamics of the homeowners’ insurance market. Using a unique dataset compiled from diverse sources, the study evaluates the future risks associated with climate-driven hurricanes and their implications for the insurance market’s stability and profitability. These findings emphasize the necessity for a dual approach- mitigating financial vulnerabilities while actively investing in long-term climate solutions.
To examine the economic implications of climate change (CC) on the insurance sector, we quantify the impact of CC-induced hurricane damages on total producer surplus (profitability). Our methodology follows a structured approach: First, we develop a theoretical framework that simulates insurance market equilibrium in response to climate-related escalations in hurricane damage. This framework is informed by historical insurance market data, climate-economic projections (Dinan 2017; Duncan & Myers 2000), and socio-economic forecasts for the end of the century. Second, we employ a comparative static analysis to estimate the resulting changes in the insurance industry’s profitability. Finally, to assess the potential role of the insurance sector in financing climate mitigation, we compare the projected decline in profitability with the share of global emission reduction targets. This final step provides an empirical basis for discussing the insurance sector’s potential as a financial aggregator for climate change mitigation, a consideration expanded upon in the Discussion section.
To assess how climate change (CC) affects the equilibrium in the homeowners’ insurance market, we employed a competitive equilibrium model initially developed for crop insurance under catastrophic risk (Duncan & Myers 2000), rooted in the Rothschild and Stiglitz (1976) framework, that accounts for correlated catastrophic risks among insureds. Recent applications of this model have extended its use to natural catastrophe insurance markets (Wu 2020), making it particularly relevant for this study.
The model characterizes a long-term equilibrium by the premium rate per policyholder w, the coverage level as a proportion of loss , and the number of policies sold by each firm n. The total number of insurers in the market can be expressed by , where N is the total number of insurance policies sold, and n is the number of policies sold by each firm. The equilibrium is derived from the simultaneous solution of three equations: short-term demand, short-term supply, and long-term supply (Duncan & Myers 2000).
Figure 1 presents the changes in a static, single-period setting. The demand (D) and supply (S) curves represent the pre-climate change equilibrium, whereas the climate-adjusted curves (D and S) reflect changes induced by increased damage caused by hurricanes. In this framework, Pins represents the premium price for a given insurance coverage, Qins. The supply curve (S) represents insurance costs per coverage unit, so as more potential damage is insured (higher coverage rate) Qins increases, so does the price per coverage unit, Pins due to heightened risk exposure. The demand curve (D) represents the utility insurers seek, and higher coverage levels typically lead to lower premiums per policyholder, as marginal utility diminishes. At equilibrium, the intersection of D and S determines the profitability of insurers (producer surplus), which is calculated as total revenue minus the area under the supply curve (representing costs).
Several simplifying assumptions were made to focus on the market equilibrium. The product traded in the insurance market coverage is assumed to be homogeneous, while insurers’ behavior is reflected in the demand function. This assumption is grounded in foundational economic models (Rothschild & Stiglitz 1976; Wilson 1977) and has been applied in more recent studies on insurance market dynamics (Djehiche & Löfdahl 2014; Kong et al. 2024). The assumption of homogeneity among insurers and using the first-order condition to identify equilibrium were adopted from Duncan and Myers and made in other previous works (Gao et al. 2016). These assumptions are crucial for analyzing market size and ensuring analytical tractability. While incorporating insurer heterogeneity could enhance the model’s robustness, it would require extensive additional theoretical and empirical work, which is beyond the scope of this study but represents an important avenue for future research.
Additionally, all agents are assumed to be risk-averse (i.e., they tend to avoid risk), with preferences expressed through a mean-variance utility function. The model does not include a liquid secondary reinsurance market, reflecting the absence of fully developed reinsurance mechanisms in the homeowners’ insurance sector. The equilibrium prices are determined using a market-clearing condition. During the initial period, insureds and insurers optimize their portfolios to maximize expected utility, and the effects of these decisions are realized at the end of the period. The risk aversion values are independent of the expected values and variance of the loss. The latter two express the environmental changes as perceived by the market participants.
The demand for insurance coverage at the premium w is given by Eq. (1), where λ is the insured’s risk aversion factor, is the expected loss, and is the variance of the loss.
Equation (1) captures the inverse relationship between premium levels and insurance demand: as premiums increase, demand declines, but an increase in expected loss, risk aversion, or damage variance increases demand. The supply is given by Eq. (2), where c stands for the insurance costs per percentage of covered damage and ψ is the insurer’s risk aversion factor. In most insurance literature, firms providing insurance are assumed to be risk-neutral (Duncan & Myers 2000). All insurers face the same marginal probability distribution for l, but the losses of each pair may be correlated. ρ stands for the correlation coefficient for any two insureds.
The supply of insurance coverage increases with premiums and declines with costs, expected loss, risk aversion, and variance of expected loss.
Generally, the long-run competitive equilibrium is characterized by zero profits achieved by the free entry and exit of firms. When risk is involved, long-run competitive equilibrium is described by zero expected profits if the producers are risk-neutral (Appelbaum & Katz 1986). The long-term competitive equilibrium, denoted by the superscript 0, is given by Eq. (3), where the reservation preference level of insurers, b, determines the entry or exit of risk-averse firms in the market:
Solving Eq. (1) for w and substituting the result into Eq. (2), the equilibrium relationship between φ and n is given by Eq. (4):
For any given n, Eq. (4) provides the equilibrium with a coverage level that equates to the demand and short-run supply of insurance.
To enhance clarity, Table 1 provides a summary of the key parameters and variables used in the model, detailing their definitions and roles within the theoretical framework.
To assess the accuracy of our theoretical model in simulating market equilibria, we assembled a unique dataset spanning the years 1997-2017, incorporating information from multiple sources. The supplementary materials comprehensively outline detailed specifications of the model parameters and assigned values, variables, and data sources (Section SM1.1 and Table SM-1).
Natural catastrophe insurance in the U.S. is traded, in addition to the commercial market, in the residual market. Residual markets are designed to provide insurance access to homeowners declined by the commercial markets in some high-risk regions. These insurance programs are backed by public funding and are, by definition, not acting as competitive markets. As the available NAIC reports included residual market data, we considered whether including residual market data would distort our analysis. To do that, we sampled data retrieved from the Property Insurance Plans Service (PIPSO). The data did not demonstrate any anomalies that might arise from including the residual market in this analysis, and hence, we carried out the analysis including the residual market data with no concerns of significant bias.
The projected values for the expected damage parameter are derived from the outcomes of three distinct models (Dinan 2017; Mendelsohn et al. 2011a), outlined in Table SM-2 in the supplementary material.
Models A and B originate in the work of Mendelsohn et al. (2011), who estimated the additional annual expected hurricane damage resulting from CC in the U.S. by the end of the twenty-first century using four Atmosphere-Ocean General Circulation Models to predict global warming scenarios under the IPCC A1B SRES emissions scenario. Two damage functions are used to estimate future values of hurricane damage. Model C originates in a follow-up study that accounted for two additional factors- coastal development and sea-level rise (S.L.R.)- in projecting changes in annual damage by the year 2075 (Dinan 2017).
Results from both studies predicted that the annual hurricane damage will increase due to CC by 0.05% of the expected U.S. GDP for 2100 by model A (Mendelsohn et al. 2011a) and 0.06% for 2075 by model C (Dinan 2017). The projected frequency of storms of category 4-5 is predicted to nearly double over the Atlantic, as reflected in the expected average damage increase (Mendelsohn et al. 2011a). Based on the modeling predictions and market practices as reflected in the past data, we estimate the insured loss expected by the agents.
The variance in hurricane damage and risk aversion is pivotal for projecting market equilibria. However, predictions of their future values are not available in the literature and fall beyond the scope of this study. Therefore, we based our analysis on the observed values and complemented it with sensitivity analyses based on the following estimates.
For the hurricane damage variance, we chose 3 values that followed an upward trend identified in the 10-year hurricane occurrences variance. This trend is further supported by the strong correlation identified with global sea surface temperature trends (at R = 0.703), as illustrated in Fig. 2. The values for hurricane damage variability used in the sensitivity analysis are increases of 20%, 250%, and 400% relative to the most recent variability in damage. Data on Atlantic tropical cyclone occurrences were sourced from the National Hurricane Center hurricane database (H.U.R.D.A.T.), and mean sea surface temperature anomalies were obtained from NOAA Extended Reconstructed Sea Surface Temperature (ERSST.v5).
We applied Arrow’s theory of risk aversion by adjusting the observed risk aversion values for the insured. Arrow theorized that individuals’ risk aversion declines as wealth increases relative to capital at risk (Arrow 1974b). While economic growth expectations are readily available as a central factor in public policy planning, the current values for risk aversion are not reported (see Supplementary Materials Section SM1.4. for further details). To estimate current values of risk aversion, we calibrated the theoretical model using observed equilibria data series. The calibrated risk aversion values for the insured population exhibited a declining trend, consistent with economic theory and economic growth, as depicted in Fig. 3. For reference, this figure also includes data on the occurrence of major hurricanes. To validate the accuracy of the range of the calibrated risk aversion values, we consider other relevant studies. For instance, studies of the Chinese crop insurance market (Shen & Odening 2013) and an experimental game design study in the E.U. (Mol et al. 2020), yielded similar values.
To estimate the model’s ability to simulate equilibria and the derived producer utility, we conducted a three-stage validation test comparing model outputs to actual profit data. The model successfully validated the employed profit function, explaining 78% of the actual profits. A full description of the validation procedure is provided in the following subsection.
Risk-averse factors are of high importance in the insurance market equilibrium and are non-trivial to estimate. As these values are market-specific, they are not commonly available in the literature. We estimated these values by calibrating the theoretical model to reflect actual equilibria and loss expectations. The resulting values for the insurer’s risk aversion ranged between 2.9 * 10 and 3.4 * 10, and for the insureds ranged between 0.01 and 0.022. Table 2 summarizes the calibrated values and literature references, brought in detail in the following subsection.
Reference values from the available literature originated in other locations and are brought to put the calibration results into context. Relevant experimental evidence for insureds (Mol et al. 2020) referred to a 5.79 risk-averse factor (for all participant groups, including ones that did not purchase any insurance, who purchased insurance with or without additional funding, and more), as well as an estimation for Chinese farmers absolute risk aversion (Shen & Odening 2013) at . The 2020 estimation (Mol et al. 2020) should be interpreted in the context in which it was obtained- a designed game, based on Experimental Currency Units (ECU) and not actual currency. To reach an estimation of relative risk aversion (that corresponds to wealth), we adjusted the estimates by 2017 EU GDP per capita (33,008$) divided by the maximum worth of ECU payoff in the game (converted to USD), which resulted in an absolute risk aversion estimate of 0.139. Once adjusted, the estimation for the US homeowner’s insurance market derived from past data is closer to the one estimated in developed countries, such as the EU, than it is to the one estimated for farmers in a developing country, with the remaining difference potentially resulting from different preferences or game design. Additionally, the scale differences between the two available literature references for insureds’ risk aversion highlight the differences in the Chinese and European economies.
For insurers, available literature provides estimates depending on the status of the reinsurance markets in terms of capital availability (Tesselaar et al. 2020) (soft and hard markets), ranging from 0.4 to 0.7, and estimation of Chinese insurers absolute risk aversion (Shen & Odening 2013) at 1.4 * 10. The model calibration results are closer to the estimation for the Chinese market made at 1.4 * 10 than it is to the one made for the EU market.
To further support the calibrated values, we turn to economic theory to confirm our estimations. The Theory of Risk Bearing (Arrow 1974b) indicates that absolute risk aversion is expected to decrease under increased wealth. As expected under economic growth, the calibrated values followed a similar clear decreasing trend for both insureds’ and insurers’ risk-aversion. Figure 3 illustrates this trend, as well as the count of major hurricanes during this period. As of the year 2005 (the hurricane season including hurricanes Katrina, Wilma, and Rita), the insurers’ absolute risk aversion was found to be correlated with the number of over a billion-dollar hurricanes, suggesting that insurers annually adjust this parameter with experience.
Although projecting future risk aversion involves many uncertain factors, we did our best to estimate it, for the demand side, by the Theory of Risk Bearing and economic growth expectations. This work theorized (Arrow 1974a) that individuals’ absolute risk aversion results from their wealth and attitude towards risk, declining as wealth increases relatively to capital at risk. This implies that generally, the observed trend is expected to continue as a result of steady economic growth. Since both economic growth and capital at risk (property value) are influenced by population growth (Baker et al. 2005), to estimate the future risk aversion, we take one step forward. We break down the economic growth to its basic elements of labor, capital, and technological development (Sredojević et al. 2016). We make a simplifying assumption that population growth will increase the demand for housing, thus will be reflected in housing prices (Jud & Winkler 2002). As labor-induced (population) growth is reflected in the value of capital at risk, it will not affect absolute risk aversion. For this reason, we estimate the decline in future risk aversion by deducting the expected population growth rate from the total expected growth rate. Due to the significant uncertainty in projecting these trends by the end of the 21 century, this analysis used the last known absolute risk aversion value (see Table 2), followed by a sensitivity analysis of the future decreased absolute risk aversion, estimated as follows:
To estimate the model’s ability to simulate equilibria and the derived producer utility, modeling results were compared to actual profits in a three-stage test on a time series of annual industry’s profits collected from NAIC’s report “Statistical Compilation of Annual Statement Information for Property/Casualty Insurance Companies” :
While actual financial results are volatile along financial years, spanning from 12 billion USD in loss to a 14 billion USD profit between 1997 and 2017 (with a standard deviation of 8.6 billion), the simulated results are much less volatile (with a standard deviation of USD 4.7 Billion in real prices), due to their dependence on a shorter past damage record.
