# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Main mathematical characteristics of payment functional

and Mazur, Stepan LU (2012) In Bulletin of the Lviv University, Series in Mechanics & Mathematics p.157-164
Abstract
The aim of our work was to calculate basic mathematical characteristics of payment functional, such as mathematical expectation, variation and expected risk in discrete and continuous market models. In our paper we present a model of financial market in which the entire time interval in the continuous model is divided into steps with exponential distribution, and in the discrete model into steps of length 1. Using the appropriate ergodic theorems for continuous and discrete Markov chains we have found the mathematical expectation, variation and expected risk. The results have theoretical and practical application in verifying the accuracy of modeling prices of derivative securities in the economy and finance.
author
publishing date
type
Contribution to specialist publication or newspaper
publication status
published
subject
keywords
stationary distribution, Markov chain, transition probabilities, option
categories
Popular Science
in
Bulletin of the Lviv University, Series in Mechanics & Mathematics
issue
18
pages
157 - 164
publisher
L'vivs'kyi Natsional'nyi Universytet imeni Ivana Franka. Mekhaniko-Matematychnyi Fakul'tet
ISSN
2078-3744
language
Other
LU publication?
no
id
2015-10-23 15:18:15
date last changed
2016-11-10 11:03:00
```@misc{86934712-b917-48e5-ad08-7c13911ab8dd,
abstract     = {The aim of our work was to calculate basic mathematical characteristics of payment functional, such as mathematical expectation, variation and expected risk in discrete and continuous market models. In our paper we present a model of financial market in which the entire time interval in the continuous model is divided into steps with exponential distribution, and in the discrete model into steps of length 1. Using the appropriate ergodic theorems for continuous and discrete Markov chains we have found the mathematical expectation, variation and expected risk. The results have theoretical and practical application in verifying the accuracy of modeling prices of derivative securities in the economy and finance.},
author       = {Yeleiko, Yaroslav and Lazariv, Taras and Mazur, Stepan},
issn         = {2078-3744},
keyword      = {stationary distribution,Markov chain,transition probabilities,option},
language     = {mis},
number       = {18},
pages        = {157--164},
publisher    = {L'vivs'kyi Natsional'nyi Universytet imeni Ivana Franka. Mekhaniko-Matematychnyi Fakul'tet},
series       = {Bulletin of the Lviv University, Series in Mechanics & Mathematics},
title        = {Main mathematical characteristics of payment functional},
year         = {2012},
}

```