Poisson Approximation of a Security Market by the Geometric Markov Renewal Processes

2016 ◽  
pp. 245-254
Keyword(s):  
Poisson Approximation ◽  
Security Market ◽  
Renewal Processes ◽  
Markov Renewal Processes

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

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Anatoliy Swishchuk ◽  
M. Shafiqul Islam
Keyword(s):  
Approximation Scheme ◽  
Option Price ◽  
Rates Of Convergence ◽  
Security Market ◽  
Renewal Processes ◽  
Call Option ◽  
Diffusion Approximations ◽  
European Call Option ◽  
Markov Renewal Processes ◽  
Diffusion Scheme

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.

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

scholarly journals Limit Theorems for Markov Renewal Processes

1964 ◽  
Vol 35 (4) ◽  
pp. 1746-1764 ◽  
Author(s):  
Ronald Pyke ◽  
Ronald Schaufele
Keyword(s):  
Limit Theorems ◽  
Renewal Processes ◽  
Markov Renewal Processes

Analysis of an M/G/1 queue with two types of impatient units

1995 ◽  
Vol 27 (03) ◽  
pp. 840-861 ◽  
Author(s):  
M. Martin ◽  
J. R. Artalejo
Keyword(s):  
Markov Chain ◽  
Performance Measures ◽  
Mathematical Analysis ◽  
Service System ◽  
Probability Distributions ◽  
Embedded Markov Chain ◽  
Renewal Processes ◽  
Stationary Probability ◽  
Markov Renewal Processes ◽  
Specific Performance

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later. We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/l type and in expressions of ‘Takács' equation' type.

On non-singular Markov renewal processes with an application to a growth–catastrophe model

1985 ◽  
Vol 22 (02) ◽  
pp. 253-266
Author(s):  
Seppo Niemi
Keyword(s):  
Markov Process ◽  
Total Variation ◽  
Population Model ◽  
Limit Theorems ◽  
Renewal Processes ◽  
Regenerative Processes ◽  
Catastrophe Model ◽  
Markov Renewal Processes ◽  
Harris Recurrence ◽  
Forward Process

The paper is concerned with Markov renewal processes satisfying a certain non-singularity condition. The relation of this condition to irreducibility, Harris recurrence and regularity of the associated forward Markov process is studied. This enables one to prove limit theorems of a total variation type for Markov renewal processes and semi-regenerative processes by applying Orey's theorem to the forward process. The results are applied to a GI/G/1 queue and a growth-catastrophe population model.

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