Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model

2016 ◽  
Author(s):  
Xiaozhen Qi
Keyword(s):  
Discrete Time ◽  
Time Dependent ◽  
Sparre Andersen Model ◽  
Andersen Model

scholarly journals Elliptic Solutions of Dynamical Lucas Sequences

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 183
Author(s):  
Michael J. Schlosser ◽  
Meesue Yoo
Keyword(s):  
Discrete Time ◽  
Time Dependent ◽  
Fibonacci Polynomials ◽  
Lucas Sequences ◽  
Elliptic Solutions

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.

scholarly journals On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model

2007 ◽  
Vol 37 (02) ◽  
pp. 203-233 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Jürgen Hartinger ◽  
Stefan Thonhauser
Keyword(s):  
Risk Model ◽  
Infinite Horizon ◽  
Threshold Level ◽  
Threshold Strategy ◽  
Sparre Andersen Model ◽  
Dividend Payments ◽  
Andersen Model ◽  
Linear Barrier ◽  
Barrier Type ◽  
Premium Income

For the classical Cramér-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.

scholarly journals Time-dependent performance analysis of a discrete-time priority queue

2008 ◽  
Vol 65 (9) ◽  
pp. 641-652 ◽  
Author(s):  
Joris Walraevens ◽  
Dieter Fiems ◽  
Herwig Bruneel
Keyword(s):  
Performance Analysis ◽  
Discrete Time ◽  
Priority Queue ◽  
Time Dependent

Elastic Interfaces for Visual Data Browsing

2006 ◽  
pp. 187-195
Author(s):  
Wolfgang Hürst
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Target Position ◽  
Rubber Band ◽  
Time Dependent ◽  
Elastic Behavior ◽  
Independent Data ◽  
Visual Data ◽  
Elastic Interfaces ◽  
Data Browsing

In this article, we discuss the concept of elastic interfaces, which was originally introduced by Masui, Kashiwagi, and Borden (1995) a decade ago for the manipulation of discrete, time-independent data. It gained recent attraction again by our own work in which we adapted and extended it in order to use it in a couple of other applications, most importantly in the context of continuous, time-dependent documents (Hürst & Götz, 2004; Hürst, Götz, & Lauer, 2004). The basic idea of an elastic interface is illustrated in Figure 1. Normally, objects are moved by dragging them directly to the target position (direct positioning). With elastic interfaces, the object follows the cursor or mouse pointer on its way to the target position with a speed s that is a function of the distance d between the cursor and the object. They are called elastic because the behavior can be explained by the rubber-band metaphor, in which the connection between the cursor and the object is seen as a rubber band: The more the band is stretched, the stronger the force between the object and the cursor gets, which makes the object move faster. Once the object and cursor come closer to each other, the pressure on the rubber band decreases, thus slowing down the object’s movement. In the next section we describe when and why elastic interfaces are commonly used and review related approaches. Afterward, we illustrate different scenarios and applications in which elastic interfaces have been used successfully for visual data browsing, that is, for skimming and navigating through visual data. First, we review the work done by Masui (1998) and Masui et al. (1995) in the context of discrete, time-independent data. Then we describe our own work, which applies the concept of elastic interfaces to continuous, time-dependent media streams. In addition, we discuss specific aspects considering the integration of such an elastic behavior into common GUIs (graphical user interfaces) and introduce a new interface design that is especially useful in context with multimedia-document skimming.

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