Author: EKATERINA TODOROVA KOLKOVSKA

BLOWUP AND LIFE SPAN BOUNDS FOR A REACTION-DIFFUSION EQUATION WITH A TIME-DEPENDENT GENERATOR

EKATERINA TODOROVA KOLKOVSKA (2008)

We consider the nonlinear equation

@

@t

u(t) = k(t)u(t) + u1+(t), u(0, x) = '(x), x 2 Rd,

where := −(−)/2 denotes the fractional power of the Laplacian; 0 <

2, , > 0 are constants; ' is bounded, continuous, nonnegative

function that does not vanish identically; and k is a locally integrable function.

We prove that any combination of positive parameters d, , , , obeying

0 < d/ < 1, yields finite time blow up of any nontrivial positive solution.

Also we obtain upper and lower bounds for the life span of the solution, and

show that the life span satisfies T' −/(−d) near = 0.

Article

Análisis Estocástico CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS PROBABILIDAD PROCESOS ESTOCÁSTICOS PROCESOS ESTOCÁSTICOS

MINIMIZING THE RUIN PROBABILITY OF RISK PROCESSES WITH REINSURANCE

EKATERINA TODOROVA KOLKOVSKA (2008)

For two combinations of proportional and excess of loss reinsurance

in a renewal risk process, we investigate existence of the insurer’s adjustment

coefficient as a function of retention levels, assuming that the premiums are

calculated according to the expected value principle. In the classical Poisson

compound case with exponentially distributed claims we prove, under some ad-

ditional assumptions, unimodality of the adjustment coefficient as a function of

the retention levels. For the maximal adjustment coefficient the ruin probabil-

ity is minimal. Our results complement previous work of Waters [8], Centeno

[3] and Hesselager [4].

Article

Teoría de Juegos Insertidumbre CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS ESTADÍSTICA ESTADÍSTICA ESTADÍSTICA