User awynjones - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T21:34:05Z http://mathoverflow.net/feeds/user/31844 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/123670/all-possible-linear-combinations-of-positive-half-integers-with-coefficients/123692#123692 Answer by awynjones for All possible linear combinations of positive half-integers with coefficients +/- 1 awynjones 2013-03-06T01:54:45Z 2013-03-06T01:54:45Z <p>Your problem is equivalent to a well-known problem in banking. Transform your problem as suggested by Per. Now imagine a bank holding a portfolio of bonds issed by obligors numbered $i=1,2,,\ldots,n$ and the bank owns bonds worth $p_1,p_2,\ldots,p_n$ issued respectively by these obligors. The $f_i$ variables correspond to indicator variables: $f_i=1$ means obligor $i$ defaulted (in a twelve month period, say), otherwise the value is 0. The value $\mu(P')$ is proportional the probability that the portfolio will sustain a loss of $P'$.</p> <p>This discrete distribution approaches a continuous curve as $n\to\infty$. There are well-known theories to estimate this curve which come under the heading "Saddlepoint Approximations". For example, see "Saddlepoint Approcimations with Applications" by Ronald Butler, publ by Cambridge Unic Press. The classic is "Saddlepoint Approximations" by Jens Lensen publ by Oxford, but it's expensive.</p> http://mathoverflow.net/questions/123227/is-there-a-statistical-interpretation-of-greens-theorem-stokes-theorem-or-the/123271#123271 Answer by awynjones for Is there a statistical interpretation of Green's theorem, Stokes' theorem, or the divergence theorem? awynjones 2013-02-28T22:03:45Z 2013-02-28T22:03:45Z <p>The gradient and div appear in maximum likelihood models in statistics and in statistical mechanics which are all used in financial mathematics.</p> http://mathoverflow.net/questions/123227/is-there-a-statistical-interpretation-of-greens-theorem-stokes-theorem-or-the/123271#123271 Comment by awynjones awynjones 2013-03-06T01:44:22Z 2013-03-06T01:44:22Z &quot;Multivariate Statistical Methods&quot; by Donald Morrison, Professor at <b>Wharton</b> publ by McGraw-Hill. A more mathematical treatment is in &quot;Multivariate Analysis&quot; Mardia, Kent, &amp; Bibby publ by Academic Press.