The Geometric Markov Renewal Processes with Application to Finance

DOI10.1080/07362994.2011.581103zbMath1223.60072OpenAlexW2021865645MaRDI QIDQ5198943

Anatoliy Swishchuk, Md. Shafiqul Islam

Publication date: 10 August 2011

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2011.581103

zbMATH Keywords

rates of convergencerandom evolutionsgeometric Markov renewal process (GMRP)averaged and double averaged GMRPmartingale properties of GMRPmerged GMRP

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Markov renewal processes, semi-Markov processes (60K15) Financial applications of other theories (91G80)

Related Items (7)

Unnamed Item ⋮ A linear spline maximum entropy method for Frobenius-Perron operators of multi-dimensional transformations ⋮ Piecewise convex deterministic dynamical systems and weakly convex random dynamical systems and their invariant measures ⋮ Diffusion approximations of the geometric Markov renewal processes and option price formulas ⋮ Discrete-Time Semi-Markov Random Evolutions and their Applications ⋮ Normal Deviation and Poisson Approximation of a Security Market by the Geometric Markov Renewal Processes ⋮ INVARIANT MEASURES FOR RANDOM MAPS VIA INTERPOLATION

Cites Work

• Contingent claims valuation when the security price is a combination of an Itō process and a random point process
• Absolutely continuous invariant measures for random maps with position dependent probabilities
• Position dependent random maps in one and higher dimensions
• Random dynamics and finance: constructing implied binomial trees from a predetermined stationary density
• Option pricing: A simplified approach
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