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¨³ œn Š „µ¦ž¦³„´œ£´ ¥ÁÈ—Á˜¨È — ¨³„µ¦ž¦³„´œ»£µ¡ °Šže°»´˜·Á®˜»š¸É¡.«. 2548 ™¹Š že °»´ ˜·Á®˜»š¸É¡.«. 2552
—´ŠÂ—ŠÄœ˜µ¦µŠš¸É1 ™¹ Š˜µ¦µŠš¸É4 ×¥Šµœª· ‹´¥œ¸ÊčoÁš‡œ·‡¼˜Â˜¦ž œ°œ¡µ¦µÁ¤˜¦·„ (Nonparametric
bootstrap technique) ×¥¼ ˜¦š¸ÉœÎµ¤µÄo‡Îµœª–‡nµÁ«¬Á®¨º° (Residuals) ‡º° ‡nµ‡¨µ—Á‡¨ºÉ°œ °Š˜´ªÁ«¬Á®¨º° °Š
Á¡¸¥¦´œ (Unstandardized Pearson Residuals) ®µÅ—o‹µ„ ˆ ˆ p
ij ij ij ij r y m m ×¥š¸É ‡nµ ij y ‡º°‡nµš¸ÉÁ¡·É¤ ¹Êœ °Š‡nµ
·œÅ®¤š—šœ °Šže°»´˜·Á®˜»š¸É i „´že¡´ •œµ„µ¦š¸É j ¨³‡nµ ˆ ij m ‡º°‡n µž¦³¤µ–š¸ÉÁ®¤µ³¤Îµ®¦´„µ¦Á¡·É¤ ¹Êœ
°Š‡nµ· œÅ®¤š—šœš¸Éže°»´˜·Á®˜»š¸É i „´že¡´ •œµ„µ¦š¸É j š¸É ‹Îµœªœ„µ¦šÎµŽÊÎ µÄœ„¦³ªœ„µ¦¼˜Â˜¦ž ‡º° 1,000
¦° ×¥Á ¸ ¥œ¢{Š„r´ÉœœÃž¦Â„¦¤ R Ĝ„µ¦ž¦³¤ª¨Ÿ¨ š¸É¦³—´œ´¥Î µ‡´š¸ÉčoĜ„µ¦ž¦³¤µ–ÁŠ·œÎµ¦°Š‡nµ
·œÅ®¤š—šœ—oª¥ª·›¸ ¼˜Â˜¦ž ¤¸‡nµ 0.05 ץ—Š ´Êœ˜°œÄœ„µ¦®µ‡n µ‡ªµ¤‡¨µ—Á‡¨ºÉ°œ¡¥µ„¦–r°Šª·›¸°¦rœ
±¼˜Áš°¦r Á¢°¦r„¼Ž´œš¸Éčoª·›¸¼˜Â˜¦ž ¤¸´Êœ˜°œÂ—ŠÅªoĜ£µ¡š¸É1 ¨³ ¤¸š§¬‘¸š¸ÉÁ„¸É¥ª o°Š„´ Šµœª·‹´¥—´ Šœ¸Ê
´Êœ˜°œš¸É 1 ´ÊœÁ˜¦¸¥¤„µ¦ (The preliminaries)
1. ž¦³¤µ–‡nµ¦¼žÂ °Š¡´•œµ„µ¦ (development pattern) 1 2 1 ˆ ˆ ˆ , , ..., n z z z 宦´ ˜µ¦µŠ¦¼žµ¤Á®¨¸É¥¤ °Š o°¤¼¨
2. ‡Îµœª–‡n µš¸ÉÁ®¤µ³¤Îµ®¦´„µ¦Á¡·É¤ ¹Êœ °Š·œÅ®¤š—šœ , ˆ i j m ×¥š¸É 1, 2,..., i n ¨³ 1, 2,..., 1 j n i
3. ‡Îµœª–‡n µÁ«¬Á®¨º° (residuals : p
ij r )
4. ž¦³¤µ–‡nµÁºÊ°Š˜oœ °Š‡nµ·œÅ®¤š—šœ¤¼¦–r (prior ultimate claims) 1 2 ˆ ˆ ˆ , ,..., n U U U 宦´˜µ¦µŠ¦¼žµ¤Á®¨¸É¥¤
°Š o°¤¼¨
5. ‡Îµœª–‡n µ·œÅ®¤š—šœ‡Š‡oµŠ 1 ˆ ˆ ˆ 1
i i n i R U Z ¨³ 2 ˆ ˆ ˆ ...n R R R
´Êœ˜°œš¸É 2 „µ¦ªœŽÊε °Š¼˜Â˜¦ž (šÎµŽÊε1,000 ¦°)
1. „µ¦ž¦³¤µ–‡nµ·œÅ®¤š—šœ
1.1 »n¤‡nµÁ«¬Á®¨º° (residuals) š¸Éŗo¤µ‹µ„ ´Êœ˜°œš¸É1 —oª¥„µ¦»n¤Â‡º œš¸É
1.2 ¦oµŠ o°¤¼¨Áš¸¥¤ (pseudo-data) —oª¥„µ¦œÎ µ‡nµÁ«¬Á®¨º°š¸Éž¦´Â¨oª (adjust residuals : p
ij r ) ¤µÄo„´
, ˆ ; 1, 2,...,i j m i n ¨³ 1, 2,..., 1 j n i ×¥ o°¤¼¨Áš¸¥¤œ¸Ê®µÅ—o‹µ„ * ˆ ˆ p
ij ij ij r m m˜
1.3 ž¦³¤µ–‡nµ¦¼žÂ °Š¡´•œµ„µ¦ (development pattern) ¨³®µ‡nµÁºÊ°Š˜oœ °Š‡nµ·œÅ®¤š—šœ¤¼¦–r (prior
ultimate claims) —oª¥ o °¤¼¨Áš¸¥¤ (pseudo-data)
1.4 ‡Îµœª–‡nµž¦³¤µ–ÁŠ·œÎµ¦°Š‡nµ·œÅ®¤š—šœ‡Š‡oµŠ 1
* * * ˆ ˆ ˆ 1
n i i i R U Z ¨³ * * *
2 ˆ ˆ ˆ ...n R R R
2. „µ¦®µÁŠ·œÎµ¦°Š‡nµ·œÅ®¤š—šœ‡Š‡oµŠ
2.1 »n¤‡nµÁ«¬Á®¨º°š¸Éž¦´Â¨oª —oª¥„µ¦»n¤Â‡ºœš¸É ץĮo‡nµÁ«¬Á®¨º°Ä®¤nš¸É ŗo ¤¸‡nµœo°¥„ªnµÁ—· ¤ ** p
ij r
2.2 ¦oµŠ‡nµš¸É‡¨oµ¥‡n µ‹¦·Š (pseudo-reality) —oª¥„µ¦œÎµ‡nµÁ«¬Á®¨º°š¸Éž¦´Â¨oª (adjust residuals) ¤µÄo
, ˆ ; 1, 2,...,i j m i n ¨³ 1, 2,..., 1 j n i ×¥‡nµš¸É‡¨oµ¥‡nµ‹¦·Šœ¸Ê ®µÅ—o‹µ„ ** ˆ ˆ p
ij ij ij r m m ˜
2.3 ž¦³¤µ–‡nµ¦¼žÂ °Š¡´•œµ„µ¦ (development pattern) ¨³®µ‡nµÁºÊ°Š˜oœ °Š‡nµ·œÅ®¤š—šœ¤¼¦–r (prior
ultimate claims) —oª¥‡n µš¸É‡¨oµ¥‡nµ‹¦·Š (pseudo- reality)
2.4 ‡Îµœª–‡nµÁŠ·œÎµ¦°Š‡nµ·œÅ®¤š—šœ‡Š‡o µŠ 1
** ** ** 1 n i i i R U Z ¨³ ** ** **
2 ... n R R R
2.5 ®µ‡ªµ¤‡¨µ—Á‡¨ºÉ°œ‹µ„„µ¦¡¥µ„¦–r ** ** * ˆ
i i i pe R R ¨³ ** ** * ˆ pe R R
´Êœ˜°œš¸É 3 ª·Á‡¦µ³®r Ÿ¨„µ¦¼˜Â˜¦ž
šÎµ„µ¦„¦³‹µ¥Á·Š¡¥µ„¦–r°ŠÁŠ·œÎµ¦°Š‡nµ·œÅ®¤š—šœ °Š i R ¨³ R ×¥„µ¦œÎµ‡nµž¦³¤µ–ÁŠ·œÎµ¦°Š¦ª¤„´
‡nµ‡¨µ—Á‡¨ºÉ°œ‹µ„„µ¦¡¥µ„¦–rš¸Éŗo‹µ„ ´Ê œ˜°œš¸É 2 ‡º° ** ** ˆ
i i i R R pe ¨³ ** ** ˆ
R R pe
£µ¡š¸É 1 ž¦³¤µ–‡nµ‡ªµ¤‡¨µ—Á‡¨ºÉ°œ¡¥µ„¦–r (prediction error) °Š‡nµž¦³¤µ–ÁŠ· œÎµ¦°Š‡nµ·œÅ®¤š—šœ °Šª·›¸°¦rœ±¼˜Áš°¦r
Á¢°¦r „¼Ž´œ (Bornhuetter-Ferguson Method) ץčoª·›¸¼˜Â˜¦ž (bootstrap method)