create new finite-state Markov chain - Maple Help

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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 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

withFinance:

P:=0.5,0.5|0.2,0.8

P:=0.50.20.50.8

(1)

X:=MarkovChainP,1.0,2.0,1,5

X:=_X

(2)

SamplePathXt,t=0..2,timesteps=10,replications=10

1..10 x 1..11 ArrayData Type: float8Storage: rectangularOrder: C_order

(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.

SamplePathXt,t=0..2,timesteps=12,replications=10

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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