ﻣﻘﺎﯾﺴﻪ ﺗﺼﺎدﻓﯽ ﻣﺠﻤﻮع ﻣﻘﺎدﯾﺮ ﺧﺴﺎرت ﻫﺎ در دو ﺳﺒﺪ ﺑﯿﻤﻪ ﻧﺎﻫﻤﮕﻦ

Stochastic Comparison of Aggregate Claim Amounts Among Two Heterogeneous Portfolios

ﻣﺠﻤﻮع ﻣﻘﺎدﯾﺮ ﺧﺴﺎرت ﻫﺎ در ﯾﮏ دوره ﺧﺎص، ﯾﮏ ﮐﻤﯿﺖ اﺳﺎﺳﯽ ﺑﺮاي ﻣﺪﯾﺮﯾﺖ ﻣﻨﺎﺳﺐ ﺷﺮﮐﺖ ﻫﺎي ﺑﯿﻤﻪ و ﻗﯿﻤﺖ ﮔﺬاري ﭘﻮﺷﺶ ﻫﺎي ﺑﯿﻤﻪ اي ﻫﺴﺘﻨﺪ. در اﯾﻦ ﻣﻘﺎﻟﻪ، ﺑﻪ ﺑﺮرﺳﯽ ﺗﺮﺗﯿﺐ ﺗﺼﺎدﻓﯽ ﻣﻌﻤﻮﻟﯽ ﺑﯿﻦ ﻣﺠﻤﻮع ﻣﻘﺎدﯾﺮ ﺧﺴﺎرت ﻫﺎ وﻗﺘﯽ ﮐﻪ ﺗﺎﺑﻊ ﺑﻘﺎي ﺧﺴﺎرت ﻫﺎ، ﺻﻌﻮدي و ﻣﻘﻌﺮ ﻫﺴﺘﻨﺪ، ﭘﺮداﺧﺘﻪ ﺷﺪه اﺳﺖ . ﺑﻪ ﻋﻼوه ﺑﺮﺧﯽ از ﻧﺘﺎﯾﺞ ﻟﯽ و ﻟﯽ )2016( ﺗﻌﻤﯿﻢ داده ﺧﻮاﻫﺪ ﺷﺪ.

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, the usual stochastic order between aggregate claim amounts is discussed when the survival function of claims is a increasing and concave. The results established here complete some results of Li and Li (2016).