ﻧﻘﺪي ﺑﺮ اﺳﺘﻔﺎده از ﺧﺴﺎرت ﻫﺎي داراي ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ در ﻣﺪل ﻫﺎي ﻣﺨﺎﻃﺮه ﺷﺮﮐﺖ ﺑﯿﻤﻪ

A Realization of Using the Claims with Pareto Distribution in Risk Models of Insurance Company

در اﯾﻦ ﻣﻘﺎﻟﻪ، ﻧﺸﺎن داده ﻣﯽ ﺷﻮد ﮐﻪ اﺳﺘﻔﺎده از ﺧﺴﺎرت ﻫﺎي داراي ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ ﺑﺮاي ﻣﺤﺎﺳﺒﻪ اﺣﺘﻤﺎﻻت ورﺷﮑﺴﺘﮕﯽ ﻣﯽ ﺗﻮاﻧﺪ ﺑﻪ ﺿﺮر ﻣﺪﯾﺮان ﺷﺮﮐﺖ ﺑﯿﻤﻪ ﺑﺎﺷﺪ. ﺑﺎ ﻣﺤﺎﺳﺒﻪ ﺧﻄﺎي ﻧﺴﺒﯽ اﯾﻦ ﺧﺴﺎر ت،ﻧﺸﺎن داده ﻣﯽ ﺷﻮد ﮐﻪ ﺑﺮآورد ﻣﯿﺎﻧﮕﯿﻦ ﺧﺴﺎرت ﻫﺎ ﺑﺮآوردي ﻣﻨﺎﺳﺐ در ﻣﺪل ﻫﺎي ﻣﺨﺎﻃﺮه ﺑﯿﻤﻪ ﻧﺨﻮاﻫﺪ ﺑﻮد. ﺧﻮاﻫﯿﻢ دﯾﺪ ﮐﻪ وﺟﻮد ﺧﺴﺎرت ﻫﺎي داراي ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ در ﻣﺪل ﺑﯿﻤﻪ اﺗﮑﺎﯾﯽ ﻣﺎزاد ﺧﺴﺎرت، ﻣﻤﮑﻦ اﺳﺖ ﺑﻪ ﺿﺮر ﺑﯿﻤﻪ ﮔﺬاران ﺷﺮﮐﺖ ﺑﺎﺷﺪ. ﻫﻢ ﭼﻨﯿﻦ در اﯾﻦ ﺳﺒﺪ ﺑﯿﻤﻪ، ﺑﺎ ﻣﺤﺎﺳﺒﻪ اﻣﯿﺪ ﺷﺮﻃﯽ ﻣﺘﻐﯿﺮ ﺗﺼﺎدﻓﯽ اﻧﺪازه ﺧﺴﺎرت،ﻧﺸﺎن داده ﻣﯽ ﺷﻮد ﮐﻪ اﺳﺘﻔﺎده از ﺧﺴﺎرت ﻫﺎي داراي ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ، ﻣﻨﺎﺳﺐ در ﺑﺮآورد ﺧﺴﺎرت ﻫﺎ ﻧﯿﺴﺖ. ﺑﺎ روش ﺷﺒﯿﻪ ﺳﺎزي، ﺑﺮآورد اﻣﯿﺪ ﺷﺮﻃﯽ ﻣﺘﻐﯿﺮ ﺗﺼﺎدﻓﯽ اﻧﺪازه ﺧﺴﺎرت ﺑﺮاي ﺑﺮﺧﯽ از ﺗﻮزﯾﻊ ﻫﺎي آﻣﺎري ﻣﺤﺎﺳﺒﻪ ﻣﯽ ﺷﻮد. ﻧﺘﺎﯾﺞ ﺑﺎ ﻣﺜﺎل ﻫﺎي واﻗﻌﯽ ﺑﺮرﺳﯽ ﻣﯽ ﺷﻮﻧﺪ.

In this paper, it is shown that using the cliams with Pareto distribution for computing the ruin probabilities could has detriment for the heads of insurance company. With computing the relative error of these cliams it is shown that the estimation of claims mean is not suitable in insurance models. We will show that existance of claims with Pareto distribution in the excess of loss reinsurance model may be detriment for the policyholders of company. Also in this portfolio, with computing the conditional expectation of claims measure show that using the claims with Pareto distribution is not suitable in the estimation of claims. The estimation of conditional expectation of random variable of claims is computed by simulation method for some of the statistical distributions. The results are investigated with real examples.