The Minimal Entropy Martingale Measure for Exponential Markov Chains

2013 ◽  
Vol 50 (02) ◽  
pp. 344-358
Author(s):  
Young Lee ◽  
Thorsten Rheinländer
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Continuous Time ◽  
Martingale Measure ◽  
Minimal Entropy Martingale Measure ◽  
Continuous Time Markov Chains ◽  
Absence Of Arbitrage

In this article we investigate the minimal entropy martingale measure for continuous-time Markov chains. The conditions for absence of arbitrage and existence of the minimal entropy martingale measure are discussed. Under this measure, expressions for the transition intensities are obtained. Differential equations for the arbitrage-free price are derived.

scholarly journals The Minimal Entropy Martingale Measure for Exponential Markov Chains

2013 ◽  
Vol 50 (2) ◽  
pp. 344-358 ◽  
Author(s):  
Young Lee ◽  
Thorsten Rheinländer
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Continuous Time ◽  
Martingale Measure ◽  
Minimal Entropy Martingale Measure ◽  
Continuous Time Markov Chains ◽  
Absence Of Arbitrage

In this article we investigate the minimal entropy martingale measure for continuous-time Markov chains. The conditions for absence of arbitrage and existence of the minimal entropy martingale measure are discussed. Under this measure, expressions for the transition intensities are obtained. Differential equations for the arbitrage-free price are derived.

A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold

1990 ◽  
Vol 22 (1) ◽  
pp. 111-128 ◽  
Author(s):  
P. K. Pollett ◽  
A. J. Roberts
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Invariant Manifold ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Centre Manifold ◽  
Continuous Time Markov Chains ◽  
Linear Differential

We use the notion of an invariant manifold to describe the long-term behaviour of absorbing continuous-time Markov processes with a denumerable infinity of states. We show that there exists an invariant manifold for the forward differential equations and we are able to describe the evolution of the state probabilities on this manifold. Our approach gives rise to a new method for calculating conditional limiting distributions, one which is also appropriate for dealing with processes whose transition probabilities satisfy a system of non-linear differential equations.

A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold

1990 ◽  
Vol 22 (01) ◽  
pp. 111-128 ◽  
Author(s):  
P. K. Pollett ◽  
A. J. Roberts
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Invariant Manifold ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Centre Manifold ◽  
Continuous Time Markov Chains ◽  
Linear Differential

We use the notion of an invariant manifold to describe the long-term behaviour of absorbing continuous-time Markov processes with a denumerable infinity of states. We show that there exists an invariant manifold for the forward differential equations and we are able to describe the evolution of the state probabilities on this manifold. Our approach gives rise to a new method for calculating conditional limiting distributions, one which is also appropriate for dealing with processes whose transition probabilities satisfy a system of non-linear differential equations.

scholarly journals Trace Machines for Observing Continuous-Time Markov Chains

2006 ◽  
Vol 153 (2) ◽  
pp. 259-277 ◽  
Author(s):  
Verena Wolf ◽  
Christel Baier ◽  
Mila Majster-Cederbaum
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Continuous Time Markov Chains
Sign in / Sign up

Export Citation Format

Share Document