Solving expressions with indicator functions in wasora

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Ramiro Vignolo

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Jul 13, 2019, 4:55:24 PM7/13/19

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Hi all,

How would you solve the following expressions within wasora’s framework:

$M = \max_{0\leq t \leq T} S(t)$ ,
$V = \mathbb{1}_{\{M > B\}} \quad \left(S(T) - K \right),$

where $T$ , $K$ and $B$ are fixed values, $S(t)$ is a wasora function and $\mathbb{1}$ is an indicator function that equals to one if the condition $M > B$ is realized and zero otherwise. This condition checks if the function crosses the barrier level at some point in time between zero and $T$ .

Let’s check out another case:

$V = \mathbb{1}_{\{S(t) > B(t)\}} \quad \left(S(T) - K \right),$

where we have substituted $B$ with a wasora function $B(t)$ and the condition must be checked in the same time interval as before, i.e., $[0, T]$ .

Other important cases are related to checks only in specific dates.

Finally, it is worth mentioning that I have already solved some cases but I would like to check out your ideas. Also, tricks using any kind of static or transient steps are not allowed.

As always, thanks a lot for reading and helping.

Rami

Jeremy Theler

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Jul 17, 2019, 5:23:54 AM7/17/19

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Here is mine

S(t) := -t^3+t^2-t+1

B(t) := t-1

K = 2

T = 5

eps = 1e-4

M = S(func_min(-S(t), t, 0, T))

V = (integral(heaviside(S(t)>B(t)), t, 0, T)>eps)*(S(T)-K)

PRINT M V

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