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Cilj ovog rada je objasniti višestruko životno osiguranje, tj. osiguranje života više osoba. U tu svrhu uvedena su zajednička stanja više osoba kao što su stanje združenih osoba, stanje posljednjeg preživjelog i opće simetrično stanje. Dokazana je Schuette-Nesbittova formula, a objašnjeni su i asimetrične rente i asimetrična osiguranja. Kako bismo se mogli posvetiti temi diplomskog rada, na početku su objašnjeni osnovni pojmovi iz područja aktuarske matematike. Također su objašnjene vrste životnog osiguranja te njihove sadašnje vrijednosti i jednokratne neto premije. Rad sadrži i objašnjenja pojmova poput životnih renti, neto premija, neto premijskih rezervi te modela višestrukih uzroka smanjenja. The main goal of this paper is to explain the multiple life insurance, ie. the life insurance of multiple person. For this purpose, common status have been introduced such as the jointlife status, the last-survivor status and the general symmetric status. The Schuette-Nesbitt formula has been proven and asymmetric rents and asymmetric insurance are explained. In order to be able to dedicate the subject of this paper, the basics of actuarial mathematics are explained at the beginning. Also, life insurance types have been explained, as well as their present values and net single premiums. The paper also includes explanations of concepts such as life annuities, net premiums, net premium reserves, and multiple decrement model.

(2009). Summations Involving Binomial Coefficients. The College Mathematics Journal: Vol. 40, No. 4, pp. 275-278.

The Dougall–Dixon summation formula is reformulated in terms of binomial sums. By computing their second derivatives, we establish several harmonic number identities.

In this article, we consider a general class of binomial models with an additional parameter λ. We show that in the case of a European call option the binomial price converges to the Black–Scholes price at the rate 1/n and, more importantly, give a formula for the coefficient of 1/n in the expansion of the error. This enables us, by making special choices for λ, to prove that convergence is smooth in Tian’s flexible binomial model and also in a new center binomial model which we propose.

An explicit formula for the inverse of the permutation character for the group action on a finite vector space is given. The proof uses a version of the binomial formula which may be new.

The binomial theorem presents us with the opportunity to weave many different mathematical strands into one lesson. It has a fascinating history — the study of which leads to a better understanding of how mathematics evolved. In this paper, we have involved computer graphics, geometry, algebra and combinatorics in the derivation of the binomial theorem. The study of functions with finite domains and ranges helps students understand some of the more subtle properties of functions which have the set of real numbers for their domain and range. These are the functions which they study to the exclusion of all others in high school and in their first two years in college. We believe that the lesson presented in this paper encourages students to express mathematical ideas in the vernacular, one of the major standards recommended by the National Council of Teachers of Mathematics (NCTM).

(1992). The Logarithmic Binomial Formula. The American Mathematical Monthly: Vol. 99, No. 7, pp. 641-648.

§1. Introduction . In 1985, Sarkozy [11] proved a conjecture of Erdos [2] by showing that the greatest square factor s ( n ) 2 of the “middle” binomial coefficient satisfies for arbitrary e > 0 and sufficiently large n Where

(1915). An Interpolation Formula for Poisson's Exponential Binomial Limit. The American Mathematical Monthly: Vol. 22, No. 7, pp. 223-224.

(1989). The Power Rule and the Binomial Formula. The College Mathematics Journal: Vol. 20, No. 4, pp. 322-322.