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Finance[MarkovChain] - create new finite-state Markov chain
Calling Sequence
MarkovChain(P, S, i, n)
Parameters
P
-
Matrix; transition matrix
S
Vector; state space
i
posint; initial state
n
posint; number of states per year
Description
The MarkovChain command creates a new finite state Markov chain.
The parameter P is the transition matrix; it must be a square matrix (see Matrix) of size , where is the number of states in the Markov chain. The value defines the probability of moving from state to state .
The parameter S is a vector containing values for all possible states of the process.
The parameter n is the number of states per year. This process can only be simulated with time steps per year, where is a positive integer. Assume for example that is a finite state Markov chain with states per year. If we simulate the process on the interval with 12 time steps, then the state change can occur only at steps , , , , and .
Compatibility
The Finance[MarkovChain] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
Examples
The following command will issue an error because the number of time steps used in simulation must be a multiple of the number of states per year.
Error, (in Finance:-SamplePath) update time .200000000000000011 does not belong to the time grid
See Also
Finance[BlackScholesProcess], Finance[CEVProcess], Finance[Diffusion], Finance[Drift], Finance[ExpectedValue], Finance[GeometricBrownianMotion], Finance[ItoProcess], Finance[PathPlot], Finance[RegimeSwitchingProcess], Finance[SamplePath], Finance[SampleValues], Finance[StochasticProcesses], Finance[WienerProcess]
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