Ex 4: exact=4.8874 bound=5.0500 ratio=0.9678 lower bound on ratio=0.9665
Ex 5: Monte Carlo=4.2474  two-state formula=4.2442
      stationary off-support probability: simulated at step 60 = 0.0751, eps/(eps+rho) = 0.0741
Ex 6: MLE reward=0.8000 shortfall=0.2000; KL-regularized (beta=1) P(good)=0.9158 shortfall=0.0842
Ex 10: J=0.6594  b*(formula)=0.5271  b*(numeric)=0.5271  Var(b*)=0.1393  Var(0)=0.3195  Var(J)=0.1506
