In auto insurance, a Bonus-Malus System (BMS) is commonly used as a posteriori risk classification mechanism to set the premium for the next contract period based on a policyholder's claim history. Even though recent literature reports evidence of a significant dependence between frequency and severity, the current BMS practice is to use a frequency-based transition rule while ignoring severity information. Although Oh et al. (2019) claim that the frequencydriven BMS transition rule can accommodate the dependence between frequency and severity, their proposal is only a partial solution, as the transition rule still completely ignores the claim severity and is unable to penalize large claims. In this study, we propose to use the BMS with a transition rule based on both frequency and size of claim, based on the bivariate random effect model, which conveniently allows dependence between frequency and severity. We analytically derive the optimal relativities under the proposed BMS framework and show that the proposed BMS outperforms the existing frequency-driven BMS. Later numerical experiments are also provided using both hypothetical and actual datasets in order to assess the effect of various dependencies on the BMS risk classification and confirm our theoretical findings.
Low visibility at an airport causes significant flight delays, thereby reducing the airport's capacity. To better understand its contributing factors, the present study examined the visibility at Incheon International Airport, South Korea, and its relationship with meteorological conditions as well as particulate matter (PM; viz., PM 2.5 and PM 10 ) concentrations for the period of 2015-2017. A censored regression model was developed to quantitatively describe the changes in visibility, and the results demonstrated that the visibility was more strongly correlated with the concentration of PM 2.5 than PM 10 . Specifically, the decrease in visibility was primarily determined by the interaction between PM 2.5 and meteorological factors, such as fog, haze, high temperatures, low relative humidity, and weak wind speed. A severe fog event during March 2018 was applied as a test case to validate this regression model, which estimated that the PM 10 and PM 2.5 impaired the visibility by approximately 8.0 km (3.2 km and 4.8 km due to PM 10 and PM 2.5 , respectively) at Incheon International Airport during hazy conditions. Our findings reveal that the concentration of PM 2.5 and its interaction with meteorological factors must be considered when diagnosing and predicting reduced visibility.
The hygroscopic property of particulate matter (PM) influencing light scattering and absorption is vital for determining visibility and accurate sensing of PM using a low-cost sensor. In this study, we examined the hygroscopic properties of coarse PM (CPM) and fine PM (FPM; PM2.5) and the effects of their interactions with weather factors on visibility. A censored regression model was built to investigate the relationships between CPM and PM2.5 concentrations and weather observations. Based on the observed and modeled visibility, we computed the optical hygroscopic growth factor, $$f\left( {RH} \right)$$
f
RH
, and the hygroscopic mass growth, $$GM_{VIS}$$
G
M
VIS
, which were applied to PM2.5 field measurement using a low-cost PM sensor in two different regions. The results revealed that the CPM and PM2.5 concentrations negatively affect visibility according to the weather type, with substantial modulation of the interaction between the relative humidity (RH) and PM2.5. The modeled $$f\left( {RH} \right)$$
f
RH
agreed well with the observed $$f\left( {RH} \right)$$
f
RH
in the RH range of the haze and mist. Finally, the RH-adjusted PM2.5 concentrations based on the visibility-derived hygroscopic mass growth showed the accuracy of the low-cost PM sensor improved. These findings demonstrate that in addition to visibility prediction, relationships between PMs and meteorological variables influence light scattering PM sensing.
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