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Finance

  

MarkovChain

  

create new finite-state Markov chain

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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 d, where d is the number of states in the Markov chain. The value Pi,j defines the probability of moving from state j to state i.

• 

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 m=nk time steps per year, where k is a positive integer. Assume for example that X is a finite state Markov chain with 3 states per year. If we simulate the process X on the interval 0..2 with 12 time steps, then the state change can occur only at steps 2, 4, 6, 8, and 10.

Examples

with(Finance):

P := <<0.5, 0.5>|<0.2, 0.8>>;

P0.50.20.50.8

(1)

X := MarkovChain(P, <1.0, 2.0>, 1, 5);

X_X0

(2)

SamplePath(X(t), t = 0..2, timesteps = 10, replications = 10);

(3)

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.

SamplePath(X(t), t = 0..2, timesteps = 12, replications = 10);

Error, (in Finance:-SamplePath) update time .200000000000000011 does not belong to the time grid

Compatibility

• 

The Finance[MarkovChain] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

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]