{"id":511,"date":"2015-01-06T17:31:03","date_gmt":"2015-01-06T17:31:03","guid":{"rendered":"http:\/\/frees.pajarel.net\/?page_id=511"},"modified":"2015-02-20T18:47:56","modified_gmt":"2015-02-21T00:47:56","slug":"example","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/5-associated-single-decrement-models\/example\/","title":{"rendered":"Example"},"content":{"rendered":"

You are given the following extract from a triple-decrement table. Calculate (l_{63}).<\/p>\n\n\n\n\n\n\n
\\(x\\)<\/td>\n\\(p_x^{01}\\)<\/td>\n\\(p_x^{02}\\)<\/td>\n\\(p_x^{03}\\)<\/td>\n\\(p_x^{0\\bullet}\\)<\/td>\n\\(l_x\\)<\/td>\n\\(q_x^{\\prime(1)}\\)<\/td>\n\\(q_x^{\\prime(2)}\\)<\/td>\n\\(q_x^{\\prime(3)}\\)<\/td>\n<\/tr>\n
60<\/td>\n0.010<\/td>\n0.050<\/td>\n0.020<\/td>\n<\/td>\n10,000<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
61<\/td>\n<\/td>\n<\/td>\n<\/td>\n0.076<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
62<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n0.033<\/td>\n0.990<\/td>\n<\/tr>\n
63<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/table>\n

Solution.<\/em><\/p>\n

For the first row, we have \\(p_{60}^{0\\bullet} = 0.01+0.05+0.02 = 0.08\\).<\/p>\n

For the second row, we have \\(l_{61} = 10000(1-0.080) = 9,200\\).<\/p>\n

For the third row, we have \\(l_{62} = 9200(1- 0.076) = 8,501\\).<\/p>\n

For the third row, we also have \\(p_{62}^{0\\bullet} = 1- (1-0.023)(1-0.033)(1-0.99) =
\n0.06468\\).<\/p>\n

For the fourth row, we have \\(l_{63} = 8501(1-0.06468) = 7,951\\).<\/p>\n\n\n\n\n\n\n
\\(x\\)<\/td>\n\\(p_x^{01}\\)<\/td>\n\\(p_x^{02}\\)<\/td>\n\\(p_x^{03}\\)<\/td>\n\\(p_x^{0\\bullet}\\)<\/td>\n\\(l_x\\)<\/td>\n\\(q_x^{\\prime(1)}\\)<\/td>\n\\(q_x^{\\prime(2)}\\)<\/td>\n\\(q_x^{\\prime(3)}\\)<\/td>\n<\/tr>\n
60<\/td>\n0.010<\/td>\n0.050<\/td>\n0.020<\/td>\n0.08<\/td>\n10,000<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
61<\/td>\n<\/td>\n<\/td>\n<\/td>\n0.076<\/td>\n9,200<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
62<\/td>\n<\/td>\n<\/td>\n<\/td>\n0.06468<\/td>\n8,501<\/td>\n<\/td>\n0.033<\/td>\n0.990<\/td>\n<\/tr>\n
63<\/td>\n<\/td>\n<\/td>\n<\/td>\n0.098<\/td>\n7,951<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/table>\n

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You are given the following extract from a triple-decrement table. Calculate (l_{63}). \\(x\\) \\(p_x^{01}\\) \\(p_x^{02}\\) \\(p_x^{03}\\) \\(p_x^{0\\bullet}\\) \\(l_x\\) \\(q_x^{\\prime(1)}\\) \\(q_x^{\\prime(2)}\\) \\(q_x^{\\prime(3)}\\) 60 0.010 0.050 0.020 10,000 61 0.076 62 0.033 0.990 63 Solution. For the …<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":509,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-8f","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/511"}],"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=511"}],"version-history":[{"count":3,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/511\/revisions"}],"predecessor-version":[{"id":778,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/511\/revisions\/778"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/509"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}