The DeterministicProcess command creates a new deterministic process. The parameter x is the value of the process. The value can be constant or time-dependent and can be given either as an algebraic expression or a procedure. A procedure defining the value of a deterministic process must accept one argument (the time) and return the corresponding value of the process. If the value is given as an algebraic expression, it must depend on a single variable.

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

$v≔\mathrm{piecewise}\left(t<1\&comma;t\&comma;\frac{1}{t}\right)$

$v≔\left\{\begin{array}{cc}t& t<1\\ \frac{1}{t}& \mathrm{otherwise}\end{array}\right.$

$G≔\mathrm{DeterministicProcess}\left(v\&comma;t\right)$

$G≔\mathrm{\_P}$

$S≔\mathrm{SamplePath}\left(G\left(t\right)\&comma;t=0..3\&comma;\mathrm{timesteps}=50\right)$

$S≔\begin{array}{c}\left[\begin{array}{ccccccccccc}0.& 0.0600000000000000& 0.120000000000000& 0.180000000000000& 0.240000000000000& 0.300000000000000& 0.360000000000000& 0.420000000000000& 0.480000000000000& 0.540000000000000& \dots \end{array}\right]\\ \hfill \text{1 × 51 Array}\end{array}$

$\mathrm{plots}\left[\mathrm{display}\right]\left(\mathrm{PathPlot}\left(S\&comma;\mathrm{timegrid}=0..3\&comma;\mathrm{gridlines}\&comma;\mathrm{thickness}=3\&comma;\mathrm{color}=\mathrm{blue}\right)\&comma;\mathrm{plot}\left(v\&comma;t=0..3\&comma;\mathrm{thickness}=3\&comma;\mathrm{color}=\mathrm{red}\right)\right)$

Glasserman, P., Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag, 2004.

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

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

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