几何马尔可夫更新过程与期权价格公式的扩散逼近

International Journal of Stochastic Analysis Pub Date : 2010-12-19 DOI:10.1155/2010/347105

A. Swishchuk, M. S. Islam

{"title":"几何马尔可夫更新过程与期权价格公式的扩散逼近","authors":"A. Swishchuk, M. S. Islam","doi":"10.1155/2010/347105","DOIUrl":null,"url":null,"abstract":"We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas\",\"authors\":\"A. Swishchuk, M. S. Islam\",\"doi\":\"10.1155/2010/347105\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.\",\"PeriodicalId\":196477,\"journal\":{\"name\":\"International Journal of Stochastic Analysis\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Stochastic Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2010/347105\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Stochastic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2010/347105","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 5

摘要

本文将几何马尔可夫更新过程作为证券市场的一个模型，在扩散近似格式下研究了该过程。给出了扩散格式下遍历几何马尔可夫更新过程的弱收敛性分析和收敛速率。我们给出了遍历、双平均和合并扩散几何马尔可夫更新过程下的欧式看涨期权定价公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas

We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Stochastic Analysis

自引率

0.00%

发文量