scholarly journals A sparse Markov chain approximation of LQ-type stochastic control problems

2016 ◽  
Vol 6 (3) ◽  
pp. 363-389 ◽  
Author(s):  
Ralf Banisch ◽  
Carsten Hartmann
Keyword(s):  
Markov Chain ◽  
Stochastic Control ◽  
Control Problems ◽  
Stochastic Control Problems ◽  
Markov Chain Approximation ◽  
Chain Approximation

A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices

1978 ◽  
Vol 15 (4) ◽  
pp. 842-847 ◽  
Author(s):  
A. Federgruen ◽  
A. Hordijk ◽  
H. C. Tijms
Keyword(s):  
Markov Chain ◽  
Stochastic Control ◽  
Metric Space ◽  
Considerable Extent ◽  
Control Problems ◽  
Stochastic Matrices ◽  
Compact Metric Space ◽  
Stochastic Control Problems ◽  
Markov Chain Theory ◽  
Chain Theory

In this paper we consider a set of denumerable stochastic matrices where the parameter set is a compact metric space. We give a number of simultaneous recurrence conditions on the stochastic matrices and establish equivalences between these conditions. The results obtained generalize corresponding results in Markov chain theory to a considerable extent and have applications in stochastic control problems.

A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices

1978 ◽  
Vol 15 (04) ◽  
pp. 842-847 ◽  
Author(s):  
A. Federgruen ◽  
A. Hordijk ◽  
H. C. Tijms
Keyword(s):  
Markov Chain ◽  
Stochastic Control ◽  
Metric Space ◽  
Considerable Extent ◽  
Control Problems ◽  
Stochastic Matrices ◽  
Compact Metric Space ◽  
Stochastic Control Problems ◽  
Markov Chain Theory ◽  
Chain Theory

In this paper we consider a set of denumerable stochastic matrices where the parameter set is a compact metric space. We give a number of simultaneous recurrence conditions on the stochastic matrices and establish equivalences between these conditions. The results obtained generalize corresponding results in Markov chain theory to a considerable extent and have applications in stochastic control problems.

scholarly journals Markov chain approximation of one-dimensional sticky diffusions

2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang
Keyword(s):  
Markov Chain ◽  
Approximate Solutions ◽  
Price Model ◽  
One Dimensional ◽  
Markov Chain Approximation ◽  
Alternative Approaches ◽  
Second Order Convergence ◽  
Chain Approximation ◽  
Matrix Exponentials ◽  
Interior Points

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.

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