Can Investment Views Explain Why People Insure Their Cell Phones But Not Their Homes?—A New Perspective on the Catastrophe Insurance Puzzle
Abstract
:1. Introduction
“there is evidence that people do not voluntarily insure themselves against natural disasters even when the rates are highly subsidized. The reasons for failure of insurance markets need to be understood, as they have important implications for policy.”
2. Related Literature
“instead of describing the chances of a 100year flood as 0.01 per year, one could note that an individual living in a particular house for 25 years faces a 0.22 chance of suffering 100year damage at least once.”
3. The Corporate View of Insurance as an Investment
3.1. LowProbability Insurance
3.2. HighProbability Insurance
3.3. Combining LowProbability and HighProbability Insurance
4. The Individual View of Insurance as an Investment
4.1. LowProbability Insurance
4.2. HighProbability Insurance
5. Combining LowProbability and HighProbability Insurance
5.1. Combining the Risk Premia for LowProbability and HighProbability Insurance
5.2. WTP for Certainty for LowProbability and HighProbability Insurance Combined
 (1)
 For the first component of the I variance term, the value of $1/{\rho}_{I}=20$ was used for the lowprobability event in Section 3.2, implying ${\rho}_{I}=0.05$. For a binary random variable, one has $Var\left({\rho}_{I}\right)={\rho}_{I}\left(1{\rho}_{I}\right)=$ $0.05\cdot 0.95=0.0475.$ Therefore, with ${E}^{2}\left({\rho}_{I}\right)={0.05}^{2}=0.0025$, the bracket amounts to 0.045.On the basis of the losses caused by ten major hurricanes10 and assuming equal probabilities of their occurrence, one obtains $Var\left({L}_{I}\right)=449\cdot {10}^{6}$ and ${E}^{2}\left({L}_{I}\right)={1240}^{2}=1.54\cdot {10}^{6}$, resulting in a value of $447.46\cdot {10}^{6}$ for the second bracket. After multiplication by 0.045, one obtains $20.14\cdot {10}^{6}$ for the product. After deduction of
 (2)
 $\left\{E\left({\rho}_{I}\right)E\left({L}_{I}\right)\right\}={\left(0.05\cdot 1240\right)}^{2}=2460$, the I component of Equation (15) amounts to $20.14\cdot {10}^{6}$.
 (3)
 For the highprobability J risk associated with the cell phone, $1/{\rho}_{J}=5$ as stated in Section 3.2. Therefore, $Var\left({\rho}_{J}\right)={\rho}_{J}\left(1{\rho}_{J}\right)=0.2\cdot 0.98=0.196$ and ${E}^{2}\left({\rho}_{J}\right)={0.2}^{2}=0.04$, so the first bracket equals 0.192. For the second bracket, the average sales price of a cell phone in 2023 was USD 790.11 On the basis of the 18 quotes listed there, the variance is $Var\left({L}_{J}\right)=\mathrm{116,843}$; therefore, the value of the second bracket amounts to $\mathrm{116,843}{\left(0.2\cdot 970\right)}^{2}=\mathrm{37,636}$, resulting in $0.196\cdot \mathrm{37,636}=7377$ for the product. After deduction of $\left\{E\left({\rho}_{J}\right)E\left({L}_{J}\right)\right\}={\left(0.2\cdot 0.2\cdot 970\right)}^{2}=1505$, one obtains 5872 for the J component of Equation (9). In all, $Var\left({\rho}_{I}{L}_{I}\right)+Var\left({\rho}_{J}{L}_{J}\right)$ amounts to $20.14\cdot {10}^{6}+5872=20.146\cdot {10}^{6}$. Multiplied by ½ and ${R}_{R}=2.5$ and divided by W = 416,000, the maximum WTP for certainty is an estimated $0.0605\cdot {10}^{3}=\mathrm{US}\$60.5$ p.a.
6. Concluding Remarks
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Notes
1  Interestingly, the terms and conditions included a clause stating that there is no payment in the case of no disaster. 
2  For instance, a purchaser of insurance may feel some regret when the covered loss does not occur even after years of having paid the annual premium. Whether this constitutes a behavioral bias is unclear because it can be derived from rational behavior reflecting a consistent preference structure Eeckhoudt et al. (2018). 
3  See, for instance, Kunreuther et al. (2001). This argument seems in conflict with Prospect Theory which predicts that very small probabilities are overestimated rather than ignored Kahneman and Tversky (1979, 1992). Yet, overestimation does not necessarily entail preventive action (such as buying insurance coverage) if the estimated probability of occurrence is still very low. 
4  See Kanhaiya et al. (2022). 
5  Assume a coin to land head (=a loss) with probability ρ and tail (=no loss) with (1 − ρ). What is E_{m}, the expected number of tosses until the first head appears? With probability ρ, m = 1 and with (1 − ρ), one obtains tail, and a new independent toss is made. Thus, E_{m} = ρ + (1 − ρ)(1 + E_{m}) which can be solved for E_{m} = 1/ρ. 
6  See note 5. 
7  See note 5. 
8  See, for instance, DataIntelo (2019). 
9  See, for instance, https://www.redfin.com/state/Florida/housingmarket, last accessed 1 December 2023. 
10  See, for instance, Insurance Information Institute (2023). 
11  See note 5. 
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Study  Possible Explanations 

(Slovic et al. 1977) 

(Kunreuther and Slovic 1978) 

(Kunreuther 1984) 

(Theil 2000) 

(Kunreuther et al. 2001) 

(Kunreuther and Pauly 2004) 

(Akter et al. 2008) 

(AntwiBoasiako 2014) 

(Pothon et al. 2019) 

(Lin 2020) 

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Hofmann, A.; Zweifel, P. Can Investment Views Explain Why People Insure Their Cell Phones But Not Their Homes?—A New Perspective on the Catastrophe Insurance Puzzle. J. Risk Financial Manag. 2024, 17, 30. https://doi.org/10.3390/jrfm17010030
Hofmann A, Zweifel P. Can Investment Views Explain Why People Insure Their Cell Phones But Not Their Homes?—A New Perspective on the Catastrophe Insurance Puzzle. Journal of Risk and Financial Management. 2024; 17(1):30. https://doi.org/10.3390/jrfm17010030
Chicago/Turabian StyleHofmann, Annette, and Peter Zweifel. 2024. "Can Investment Views Explain Why People Insure Their Cell Phones But Not Their Homes?—A New Perspective on the Catastrophe Insurance Puzzle" Journal of Risk and Financial Management 17, no. 1: 30. https://doi.org/10.3390/jrfm17010030