817 research outputs found
the Transformation of Sieve Function
In this paper, we will introduce the transformation of sieve function to
improve sieve method. The sieve function can be transformed to similar sieve
function and keep its value constant. However, the error terms of sieve
function can be changed to smaller, even to be zero, such that the sieve
function can be transformed to the calculable sieve function. Using this sieve
method, Goldbach Conjecture and the Twin Prime Conjecture will be proved to be
true.Comment: 7 page
Interplay of insurance and financial risks in a discrete-time model with strongly regular variation
Consider an insurance company exposed to a stochastic economic environment
that contains two kinds of risk. The first kind is the insurance risk caused by
traditional insurance claims, and the second kind is the financial risk
resulting from investments. Its wealth process is described in a standard
discrete-time model in which, during each period, the insurance risk is
quantified as a real-valued random variable equal to the total amount of
claims less premiums, and the financial risk as a positive random variable
equal to the reciprocal of the stochastic accumulation factor. This risk model
builds an efficient platform for investigating the interplay of the two kinds
of risk. We focus on the ruin probability and the tail probability of the
aggregate risk amount. Assuming that every convex combination of the
distributions of and is of strongly regular variation, we derive some
precise asymptotic formulas for these probabilities with both finite and
infinite time horizons, all in the form of linear combinations of the tail
probabilities of and . Our treatment is unified in the sense that no
dominating relationship between and is required.Comment: Published at http://dx.doi.org/10.3150/14-BEJ625 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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