adjusting bumped mc example

Author: aleCombi

examples/bumped_montecarlo.jl

@@ -12,22 +12,21 @@ tspan = (t0, T)
 N = 250
 dt = (T - t0) / N
 
-# Step 1: Simulate base GBM and save the noise
+# Step 1: Simulate GBM with a fixed seed
 gbm = GeometricBrownianMotionProcess(μ, σ, t0, W0)
 gbm_noise = NoiseProblem(gbm, tspan, seed=1)
 sol = DifferentialEquations.solve(gbm_noise, dt=dt)
 
-# Step 2: Reuse the noise and simulate with bumped μ
+# Step 2: Reuse the same seed with bumped σ
 μ_bumped = μ
-σ_bumped = σ + 0.1
+σ_bumped = σ + 0.05
 gbm_bumped = GeometricBrownianMotionProcess(μ_bumped, σ_bumped, t0, W0)
 gbm_bumped_noise = NoiseProblem(gbm_bumped, tspan, seed=1)
-ensemble_problem_bumped = EnsembleProblem(gbm_bumped_noise)
 sol_bumped = DifferentialEquations.solve(gbm_bumped_noise, dt=dt)
 
 # Step 3: Plot both
 plot(sol.t, sol.u, label="μ = $μ", linewidth=2)
 plot!(sol_bumped.t, sol_bumped.u, label="μ = $μ_bumped", linestyle=:dash, linewidth=2)
 xlabel!("Time")
 ylabel!("GBM Value")
-title!("GBM with Drift Bump and Reused Noise")
+title!("GBM with Drift Bump and Reused Seed")