Continuous-Time Markov Models

2010 ◽  
pp. 85-145 ◽  
Author(s):  
V. G. Kulkarni
Keyword(s):  
Continuous Time ◽  
Markov Models

scholarly journals Pricing and risk management under multivariate switching models

2021 ◽  
Author(s):  
Atousa Assadihaghi
Keyword(s):  
Monte Carlo ◽  
Continuous Time ◽  
Value At Risk ◽  
Markov Models ◽  
Risk Measures ◽  
Occupation Times ◽  
Taylor Expansions ◽  
Switching Regime ◽  
Switching Models ◽  
Analytic Expressions

The objective of this thesis is to provide a simulations-free approximation to the price of multivariate derivatives and for the calculation of risk measures like Value at Risk (VaR). The first chapters are dedicated to the pricing of multivariate derivatives. In particular we focus on multivariate derivatives under switching regime Markov models. We consider the cases of two and three states of the switching regime Markov model, and derive analytic expressions for the first and second order moments of the occupation times of the continuous-time Markov process. Then we use these expressions to provide approximations for the derivative prices based on Taylor expansions. We compare our closed form approximations with Monte Carlo simulations. In the last chapter we also provide a simulations-free approximation for the VaR under a switching regime model with two states. We compare these VaR estimations with those obtained using Monte Carlo.

Clustering of Bursts of Openings in Markov and Semi-Markov Models of Single Channel Gating

1997 ◽  
Vol 29 (01) ◽  
pp. 92-113 ◽  
Author(s):  
Frank Ball ◽  
Sue Davies
Keyword(s):  
Markov Chain ◽  
Ion Channel ◽  
State Space ◽  
Continuous Time ◽  
Markov Models ◽  
Numerical Study ◽  
Channel Gating ◽  
Markov Renewal Process ◽  
Time Interval ◽  
Continuous Time Markov Chain

The gating mechanism of a single ion channel is usually modelled by a continuous-time Markov chain with a finite state space. The state space is partitioned into two classes, termed ‘open’ and ‘closed’, and it is possible to observe only which class the process is in. In many experiments channel openings occur in bursts. This can be modelled by partitioning the closed states further into ‘short-lived’ and ‘long-lived’ closed states, and defining a burst of openings to be a succession of open sojourns separated by closed sojourns that are entirely within the short-lived closed states. There is also evidence that bursts of openings are themselves grouped together into clusters. This clustering of bursts can be described by the ratio of the variance Var (N(t)) to the mean[N(t)] of the number of bursts of openings commencing in (0, t]. In this paper two methods of determining Var (N(t))/[N(t)] and limt→∝Var (N(t))/[N(t)] are developed, the first via an embedded Markov renewal process and the second via an augmented continuous-time Markov chain. The theory is illustrated by a numerical study of a molecular stochastic model of the nicotinic acetylcholine receptor. Extensions to semi-Markov models of ion channel gating and the incorporation of time interval omission are briefly discussed.

An S-Plus Implementation of Hidden Markov Models in Continuous Time

2000 ◽  
Vol 9 (4) ◽  
pp. 621 ◽  
Author(s):  
Alexandre Bureau ◽  
James P. Hughes ◽  
Stephen C. Shiboski
Keyword(s):  
Hidden Markov Models ◽  
Continuous Time ◽  
Markov Models ◽  
Hidden Markov

ENHANCING SAFETY IN SHIP'S CRITICAL SYSTEMS USING MARKOV MODELING

2009 ◽  
Vol 16 (01) ◽  
pp. 59-72
Author(s):  
EVANGELOS MENNIS ◽  
AGAPIOS PLATIS ◽  
NIKITAS NIKITAKOS ◽  
JEAN GUY FONTAINE
Keyword(s):  
Continuous Time ◽  
Markov Models ◽  
Markov Modeling ◽  
Critical Systems ◽  
System Failures ◽  
Reliability Models ◽  
Sea Pollution ◽  
System A ◽  
Bilge Water ◽  
Water Separator

The current study uses reliability models for the improvement of the operation of a ship's "bilge — water separator" system. A "bilge-water separator" is a mechanism which cleans and inspects the ship's bilge water before it is discharged into the sea. Homogeneous continuous time Markov models have been used to record and estimate possible hazards and system failures in two different operational scenarios. If the photocell unit of the system fails, the ship may cause severe sea pollution. This study attempts to estimate the probability of sea pollution based on empirical data. In addition, the results of the model are compared with those of a system in which a second metering unit is added in an effort to to find out if this alteration improves the systems' efficiency.

scholarly journals Particle filtering for continuous-time hidden Markov models

2007 ◽  
Vol 19 ◽  
pp. 12-17 ◽  
Author(s):  
Nicolas Chopin ◽  
Elisa Varini
Keyword(s):  
Hidden Markov Models ◽  
Continuous Time ◽  
Particle Filtering ◽  
Markov Models ◽  
Hidden Markov
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