{"id":492,"date":"2015-01-06T17:00:06","date_gmt":"2015-01-06T17:00:06","guid":{"rendered":"http:\/\/frees.pajarel.net\/?page_id=492"},"modified":"2015-02-20T18:38:14","modified_gmt":"2015-02-21T00:38:14","slug":"excerpt-from-a-critical-illness-multiple-decrement-table","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/3-multiple-decrement-tables\/excerpt-from-a-critical-illness-multiple-decrement-table\/","title":{"rendered":"Excerpt from a Critical Illness Multiple Decrement Table"},"content":{"rendered":"

AMLCR Example 8.9.<\/strong> The following table is an excerpt from a multiple decrement table for an insurance policy offering benefits on death or diagnosis of critical illness. The insurance expires on the earliest event of death \\(j=1\\), surrender \\(j=2\\), and critical illness diagnosis \\(j=3\\).<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\\(x\\)<\/td>\n\\(l_x\\)<\/td>\n\\(d_x^{(1)}\\)<\/td>\n\\(d_x^{(2)}\\)<\/td>\n\\(d_x^{(3)}\\)<\/td>\n<\/tr>\n
40<\/td>\n100,000<\/td>\n51<\/td>\n4,784<\/td>\n44<\/td>\n<\/tr>\n
41<\/td>\n95,121<\/td>\n52<\/td>\n4,526<\/td>\n47<\/td>\n<\/tr>\n
42<\/td>\n90,496<\/td>\n53<\/td>\n4,268<\/td>\n50<\/td>\n<\/tr>\n
43<\/td>\n86,125<\/td>\n54<\/td>\n4,010<\/td>\n53<\/td>\n<\/tr>\n
44<\/td>\n82,008<\/td>\n55<\/td>\n3,753<\/td>\n56<\/td>\n<\/tr>\n
45<\/td>\n78,144<\/td>\n56<\/td>\n3,496<\/td>\n59<\/td>\n<\/tr>\n
46<\/td>\n74,533<\/td>\n57<\/td>\n3,239<\/td>\n62<\/td>\n<\/tr>\n
47<\/td>\n71,175<\/td>\n57<\/td>\n2,983<\/td>\n65<\/td>\n<\/tr>\n
48<\/td>\n68,070<\/td>\n58<\/td>\n2,729<\/td>\n67<\/td>\n<\/tr>\n
49<\/td>\n65,216<\/td>\n58<\/td>\n2,476<\/td>\n69<\/td>\n<\/tr>\n
50<\/td>\n62,613<\/td>\n58<\/td>\n2,226<\/td>\n70<\/td>\n<\/tr>\n<\/table>\n

(a) Calculate (i) \\(_3 p_{45}^{00}\\), (ii) \\(p_{40}^{01}\\) and (iii)\\(_5 p_{41}^{03}\\).
\nSolution.<\/em>
\n\\begin{eqnarray*}
\n_3 p_{45}^{00} = \\frac{l_{48}}{l_{45}}=\\frac{68,070}{78,144}= 0.871084.
\n\\end{eqnarray*}
\n\\begin{eqnarray*}
\np_{40}^{01} &=& \\frac{d_{40}^{(1)}}{l_{40}}=\\frac{51}{100,000}= 0.00051.
\n\\end{eqnarray*}
\n\\begin{eqnarray*}
\n_5 p_{41}^{03}&=& \\frac{d_{41}^{(3)}+d_{42}^{(3)}+d_{43}^{(3)}+d_{44}^{(3)}+d_{45}^{(3)}}{l_{41}} \\\\
\n&=& \\frac{47+50+53+56+59}{95,121} = \\frac{265}{95,121} = 0.002786.
\n\\end{eqnarray*}
\n(b) Calculate the probability that a policy issued to a life aged 45 generates a claim for death or critical illness before age 47.
\nSolution.<\/em>
\n\\begin{eqnarray*}_2 p_{45}^{01}+_2 p_{45}^{03}&=& \\frac{d_{45}^{(1)}+d_{46}^{(1)}+d_{45}^{(3)}+d_{46}^{(3)}}{l_{45}} \\\\
\n&=& \\frac{56+57+59+62}{78,144} = \\frac{234}{78,144} = 0.002994.
\n\\end{eqnarray*}
\n(c) Calculate the probability that a policy issued to a life age 40 is surrendered between ages 45 and 47.
\nSolution.<\/em>
\n\\begin{eqnarray*}
\n_5 p_{40}^{00} \\times _2 p_{45}^{02}&=& \\frac{l_{45}}{l_{40}} \\times \\frac{d_{45}^{(2)}+d_{46}^{(2)}}{l_{45}}\\\\
\n&=& \\frac{d_{45}^{(2)}+d_{46}^{(2)}}{l_{40}} = \\frac{3,496+3,239}{100,000} = 0.06735.
\n\\end{eqnarray*}<\/p>\n

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AMLCR Example 8.9. The following table is an excerpt from a multiple decrement table for an insurance policy offering benefits on death or diagnosis of critical illness. The insurance expires on the earliest event of …<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":478,"menu_order":1,"comment_status":"closed","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-7W","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/492"}],"collection":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/comments?post=492"}],"version-history":[{"count":3,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/492\/revisions"}],"predecessor-version":[{"id":753,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/492\/revisions\/753"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/478"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}