Changes in reserves are expenses to a company and using a larger net premium basis can mean large expenses that may penalize smaller, fast-growing companies. Thus, a number of modified premium reserve bases have been introduced over the years, the most commonly used one being the<\/p>\n
Full Preliminary Term Approach.<\/strong> Let \\(P^n\\) be the valuation net premium that we assume level for now. Further, define, for valuation purposes,<\/p>\n * \\(_1 P_{[x]}^n = b_1 v q_{[x]} \\) a modified first year cost of insurance and The idea is the \\(P^n – _1 P_{[x]}^n\\) is the additional first year expense allowance. Thus, we have \\( 0 \\leq _1 P_{[x]}^n \\leq P^n \\leq P^{FPT}\\).<\/p>\n Let \\(h\\) be the number of premium-payment periods and \\(j\\) \\((\\leq h)\\) be the number of years that \\(P^{FPT}>P^n\\). Then, With this \\(V_k^{FPT} = V_k^n, k\\ge j\\), that is, the full preliminary term reserve equals the net premium reserve when the premiums are the same. For \\(1 \\le k < j\\), we have\n\\begin{eqnarray*}\nV_k^{FPT} = \\textrm{EPV Future Benefits} - P^{FPT} \\ddot{a}_{[x]+k:\\overline{j-k|}} - P^n ~_{j-k|h-j} \\ddot{a}_{[x]+k} .\n\\end{eqnarray*}\nThus, for \\(1 \\le k < j\\) we have \\( V_k^{FPT} < V_k^n\\) and\n\\begin{eqnarray*}\nV_k^n - V_k^{FPT}& =& \\left\\{\\textrm{EPV Future Benefits} - P^{FPT} \\ddot{a}_{[x]+k:\\overline{k-j|}} - P^n ~_{j-k|h-j} \\ddot{a}_{[x]+k} \\right\\}\\\\\n& ~~~ -& \\left\\{\\textrm{EPV Future Benefits} - P^n \\ddot{a}_{[x]+k:\\overline{k-j|}} - P^n ~_{j-k|h-j} \\ddot{a}_{[x]+k} \\right\\} \\\\\n& = & (P^{FPT}- P^n) \\ddot{a}_{[x]+k:\\overline{k-j|}} .\n\\end{eqnarray*}\nWe can think of the modified reserve \\(V_k^{FPT}\\) as the net premium reserve minus a reserve for the unamortized excess premium. \n\n[previous][next]\n<\/p>\n","protected":false},"excerpt":{"rendered":" Changes in reserves are expenses to a company and using a larger net premium basis can mean large expenses that may penalize smaller, fast-growing companies. Thus, a number of modified premium reserve bases have been …<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":326,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-5i","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/328"}],"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=328"}],"version-history":[{"count":4,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/328\/revisions"}],"predecessor-version":[{"id":848,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/328\/revisions\/848"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/326"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n * \\(P^{FPT}\\) a modified premium for subsequent years.<\/p>\n
\n\\begin{eqnarray*}
\n_1 P_{[x]}^n + P^{FPT} a_{x:\\overline{j-1|}} = P^n \\ddot{a}_{x:\\overline{j|}} .
\n\\end{eqnarray*}
\nThis is equivalent to considering splitting the policy into two components, a 1-year term and a separate contract issued to the same life one year later, if the life survives.<\/p>\n