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Stable solutions to homogeneous difference-differential equations with constant coefficients: Analytical instruments and an application to monetary theory

Ulf von Kalckreuth, Manfred Krtscha (2004)

Applications of Mathematics

In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we...

Stable-1/2 bridges and insurance

Edward Hoyle, Lane P. Hughston, Andrea Macrina (2015)

Banach Center Publications

We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the...

Standard and nonstandard representability of positive uncertainty orderings

Andrea Capotorti, Giulianella Coletti, Barbara Vantaggi (2014)

Kybernetika

Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.

Stationary and convergent strategies in Choquet games

François G. Dorais, Carl Mummert (2010)

Fundamenta Mathematicae

If Nonempty has a winning strategy against Empty in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows Nonempty to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits Nonempty to consider the previous move by Empty. We show that Nonempty has a stationary winning strategy for every second-countable T₁ Choquet space. More generally, Nonempty has a stationary winning strategy for...

Stochastic control optimal in the Kullback sense

Jan Šindelář, Igor Vajda, Miroslav Kárný (2008)

Kybernetika

The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector ( u 1 , x 1 , ... , u T , x T ) on a sample space of 2 T dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of x τ given u 1 , x 1 , ... , u τ - 1 , x τ - 1 , u τ are known for τ = 1 , ... , T . Our objective is to determine the remaining conditional probability distributions of u τ given u 1 , x 1 , ... , u τ - 1 , x τ - 1 such...

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