# Euler discretization with jumps

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.