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1.
MATEMATIČNE OSNOVE POZAVAROVANJA
Mihael Pisanec, 2011, undergraduate thesis

Abstract: V uvodnem poglavju so predstavjene osnove verjetnostnega računa. Te so prilagojene (z označbami in obliko) za nadaljna poglavja. V drugem poglavju je osrednja tema število škodnih primerov. Ta števila opišemo v smislu slučajne spremenljivke. Nastavimo enačbe za izračun osnovnih karakteristik števila škodnih primerov, katere bomo kasneje potrebovali za konstrukcijo porazdelitvene funkcije. V naslednjem poglavju s pomočjo slučajne sestavljene spremenljivke opišemo višino škod. Opišemo, kako lahko izračunamo osnovne karakteristike te slučajne spremenljivke. Slednje uporabljamo za konstrukcijo porazdelitvene funkcije velikosti škod. Uvedemo pomoţno spremenljivko, s katero lahko različno vplivamo na te porazdelitvene funkcije. Porazdelitvena funkcija nam ponazarja porazdelitev višine škod v procentih. Zaradi tega vpeljemo funkcijo limitne pričakovane vrednosti, ki nam prikazuje porazdelitev višine škod v denarnih enotah. Na koncu poglavja opišemo gamma, log-normalno in pareto porazdelitveno funkcijo, saj se te navadno uporabljajo v zavarovalništvu za predstavitev porazdelitve velikosti škod. V zadnjem poglavju je opisano, kaj pojem pozavarovanje predstavlja. Predstavljeni so različni pozavarovalni programi: kvotno (angl. quota share), vsotopreseţkovno (angl. surplus), škodnopreseţkovno (angl. excess of loss),... Nato uporabimo pridobljeno znanje iz prejšnjih poglavih za izračun osnovnih pozavarovalnih premij.
Keywords: pozavarovanje, neproporcionalno pozavarovanje, proporcionalno pozavarovanje, osnove statistike
Published: 14.11.2011; Views: 1202; Downloads: 198
.pdf Full text (1,32 MB)

2.
Time sensitivity of the Black-Scholes delta in discrete time
Miklavž Mastinšek, 2008, published scientific conference contribution

Abstract: In the case of discrete trading the Black-Scholes options delta sensitivity with respect to movements of the stock price has been widely considered in the theory and practice, while the option's delta sensitivity with respect to time has been rarely considered. The objective of this paper is to analyze the time sensitivity of delta in discrete time.An example of the European call option is given. In the case where the delta is more sensitive with respect to time a simple explicit formula for a discrete time Black-Scholes delta is provided. The order of the hedging error is preserved. In many cases the absolute value of the hedging error can be reduced.
Published: 28.05.2012; Views: 551; Downloads: 44
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3.
Stability conditions for abstract functional differential equations in Hilbert space
Miklavž Mastinšek, 2003, original scientific article

Abstract: Stability conditions for functional differential equations of the form: du (t)/dt = Au(t) + bAu(t-h) + (a*Au)(t) are studied, where A is the infinitesimal generator of an analytic semigroup in a Hilbert space, b # 0 and the convolution term contains a square integrable real function a # 0. Norm discontinuity of the solution semigroup of the equation with discrete delay is avoided by studying the inverse of the characteristic operator. Sufficient and necessary conditions for the uniform exponential stability of the solution semigroup are obtained. The results are applied to a retarded partial integrodifferential equation.
Published: 02.06.2012; Views: 625; Downloads: 72
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4.
The discrete Black-Scholes partial differential equation
Miklavž Mastinšek, 2004, published scientific conference contribution abstract

Keywords: diferencialne enačbe, enačbe, matematika, ekonomija, ekonometrija
Published: 10.07.2015; Views: 379; Downloads: 16
URL Link to full text

5.
Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spaces
Miklavž Mastinšek, 1994, original scientific article

Abstract: The paper deals with semigroups of operators associated with delay differential equation: ▫$dot{x}=Ax(t)+L_1x(t-h)+L_2x_t$▫, where ▫$A$▫ is the infinitesimal generator of an analytic semigroup on a Hilbert space ▫$X$▫ and ▫$L_1$▫, ▫$L_2$▫ are densely defined closed operators in ▫$X$▫ and ▫$L^2(-h,0;X)$▫ respectively. The adjoint semigroup of the solution semigroup of the delay differential equation is characterized. Eigenspaces of the generator of the adjoint semigroup are studied and the identifiability of parameters of the equation is given.
Keywords: matematika, analiza, navadne diferencialne enačbe, polgrupe operatorjev, diferencialne enačbe z zakasnitvijo, polgrupe rešitev, adjungirane polgrupe, prepoznavnost
Published: 10.07.2015; Views: 296; Downloads: 24
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