The RegimeSwitchingProcess command creates a regime-switching process with the specified regimes and transition probability. Each of the regimes must be a one-dimensional stochastic process. The parameter S defines all possible regimes that are one-dimensional stochastic processes. Moves between different regimes are assumed to be governed by the $d\times d$ transition probability matrix, P, with generic element $P_{j,k}$ defined as the probability of moving from regime $k$ to regime $j$.

The parameter n is the number of regimes per year. This process can only be simulated with $m$ time steps per year, where $m$ is a multiple of n. Assume for example that $X$ is a finite state Markov chain with $3$ regimes per year. If we simulate the process $X$ on the interval $0..2$ with 12 time steps, then the regime change can occur only at steps $2$, $4$, $6$, $8$, and $10$.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$P≔⟨⟨0.5\,0.5⟩|⟨0.2\,0.8⟩⟩$

$P≔\left[\begin{array}{cc}0.5& 0.2\\ 0.5& 0.8\end{array}\right]$

$S≔\left[\mathrm{BrownianMotion}\left(0\,0\,2.0\right)\,\mathrm{BrownianMotion}\left(0\,0.5\,0.001\right)\right]\:$

$X≔\mathrm{RegimeSwitchingProcess}\left(P\,S\,1\,2\right)\:$

$\mathrm{PathPlot}\left(X\left(t\right)\,t=0..2\,\mathrm{timesteps}=20\,\mathrm{replications}=10\,\mathrm{gridlines}=\mathrm{true}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{color}=\mathrm{red}..\mathrm{blue}\right)$

$P≔⟨⟨0.5\,0.5⟩|⟨0.2\,0.8⟩⟩$

$P≔\left[\begin{array}{cc}0.5& 0.2\\ 0.5& 0.8\end{array}\right]$

$S≔\left[\mathrm{BrownianMotion}\left(0\,0\,2.0\right)\,0.5t\right]$

$S≔\left[\mathrm{\_X3}\,0.5t\right]$

$X≔\mathrm{RegimeSwitchingProcess}\left(P\,S\,1\,2\,t\right)$

$X≔\mathrm{\_X4}$

$\mathrm{PathPlot}\left(X\left(t\right)\,t=0..2\,\mathrm{timesteps}=20\,\mathrm{replications}=10\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\,\mathrm{color}=\mathrm{red}..\mathrm{blue}\right)$

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

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