There is a process

$B_t = B_0\prod_{i=1}^{N_t}(1-Z_n)$,

where $Z_n=e^{-ξ_n}$ for i.i.d exponentially distributed random variables $(ξn)_{n≥1}$ with rate $ρ=20$.

${N_t}$ is a counting process with intensity $λ_t$ which solves the stochastic differential equation

$dλ_t = 0.5 (0.3 − λ_t) dt + 0.3dN_t$(a Hawkes Process) and $λ_0 = 0$.

How can I use Euler discretization scheme to generate sample paths of $B_t$ for t ∈ [0, 10]? Assume that the number of Euler steps per unit of time is 100 and $B_0$ = 10, 000.


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