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Generalized CreditRisk+ model and applications

Jakub Szotek (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In the paper we give a mathematical overview of the CreditRisk+ model as a tool used for calculating credit risk in a portfolio of debts and suggest some other applications of the same method of analysis.

Generalized duration measures in a risk immunization setting. Implementation of the Heath-Jarrow-Morton model

Alina Kondratiuk-Janyska, Marek Kałuszka (2006)

Applicationes Mathematicae

The aim of this paper is to set different lower bounds on the change of the expected net cash flow value at time H > 0 in general term structure models, referring to the studies of Fong and Vasiček (1984), Nawalkha and Chambers (1996), and Balbás and Ibáñez (1998) among others. New immunization strategies are derived with new risk measures: generalized duration and generalized M-absolute of Nawalkha and Chambers, and exponential risk measure. Furthermore, examples of specific one-factor HJM models...

Generated fuzzy implications and fuzzy preference structures

Vladislav Biba, Dana Hliněná (2012)

Kybernetika

The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet ( p , i , j ) , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.

Gini indices and the moments of the share density function

Petr Zizler (2014)

Applications of Mathematics

The expected value of the share density of the income distribution can be expressed in terms of the Gini index. The variance of the share density of the income distribution is interesting because it gives a relationship between the first and the second order Gini indices. We find an expression for this variance and, as a result, we obtain some nontrivial bounds on these Gini indices. We propose new statistics on the income distribution based on the higher moments of the share density function. These...

Growth-optimal portfolios under transaction costs

Jan Palczewski, Łukasz Stettner (2008)

Applicationes Mathematicae

This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depends on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained...

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