{"id":309,"date":"2014-12-31T15:29:54","date_gmt":"2014-12-31T21:29:54","guid":{"rendered":"http:\/\/frees.pajarel.net\/?page_id=309"},"modified":"2015-02-20T19:20:07","modified_gmt":"2015-02-21T01:20:07","slug":"2-asset-shares","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/emerging-costs\/2-asset-shares\/","title":{"rendered":"2. Asset Shares"},"content":{"rendered":"

The asset share<\/em> of a policy in force is the share of the insurer’s assets attributable to that policy. Here, expenses, interest, mortality and so forth are calculated based on the insurer’s experience for similar policies over the period.<\/p>\n

Asset share calculations are similar to those used for policy values although the purposes of the two concepts are quite different. The policy value represents an amount the insurer needs to have<\/em>, the asset share represents the amount that the insurer actually does have<\/em>.<\/p>\n

Asset shares are typically calculated recursively, such as using a relationship similar to those for policy values, e.g.,
\n\\begin{eqnarray*}
\n(~_k AS + G_k – e_k)(1+i_k) &= &
\nq_{[x]+k}^{(d)} \\left(b_{k+1} + E_{k+1}\\right) + q_{[x]+k}^{(w)} ~_{k+1} CV \\\\
\n&~~~~~~~~~~+& p_{[x]+k}^{(\\tau)} ~_{k+1} AS
\n\\end{eqnarray*}
\nwhere
\n * at the beginning of the year, \\( ~_k AS\\) is the asset share, \\(G_k\\) is the contract premium, \\(e_k\\) are annual expenses per contract
\n * at death, \\(q_{[x]+k}^{(d)}\\) is the probability of death, \\(b_{k+1}\\) is the insurance benefit, and \\(E_k\\) are settlement expenses per contract
\n * at withdrawal, \\(q_{[x]+k}^{(w)}\\) is the probability of withdrawal, \\(~_{k+1} CV\\) is the cash value,
\n * at survival to the end of the year, \\(p_{[x]+k}^{(\\tau)} = 1 – (q_{[x]+k}^{(d)}+q_{[x]+k}^{(w)})\\) is the probability of survivorship and \\( ~_{k+1} AS\\) is the asset share.<\/p>\n

Asset shares define the notion of how quickly a policy builds policy values (assets) and hence profits.<\/p>\n

The main advantage of this recursive approach is that we can examine the incidence (timing) of profits.<\/p>\n

The recursive relation can be expanded to include other ancillary benefits, taxes, more complex expense structures, and so forth.<\/p>\n

Asset shares are primarily used to set premiums by defining a profit goal. Here are some sample profit goals:<\/p>\n

* PV(profit) = \\(x\\)% PV (premium)
\n * A return on investment = \\(x\\)%
\n * The product breaks even \\(n\\) years or sooner.<\/p>\n

Asset shares can easily be used for flexible (variable) plans.<\/p>\n

They can also be used to determine reserves, dividend schedules, withdrawal benefits or so-called “model offices” (combining asset shares over several plans, age at issue, new versus old business, and so on).<\/p>\n

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The asset share of a policy in force is the share of the insurer’s assets attributable to that policy. Here, expenses, interest, mortality and so forth are calculated based on the insurer’s experience for similar …<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":302,"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-4Z","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/309"}],"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=309"}],"version-history":[{"count":5,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/309\/revisions"}],"predecessor-version":[{"id":1661,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/309\/revisions\/1661"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/302"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}