This paper examines a class of barrier options, multi-step which can have any finite number barriers level. We obtain general, explicit expression for option prices this type under the Black–Scholes model by deriving reflection principle, that is, boundary-crossing probability Brownian motion. Multi-step options are not only useful in they handle different levels and time steps but also approxi...

This paper investigates the rate of convergence of an alternative approximation method for stochastic differential equations. The rates of convergence of the one-step and multi-step approximation errors are proved to be O((∆t)2) and O(∆t) in the Lp sense respectively, where ∆t is discrete time interval. The rate of convergence of the one-step approximation error is improved as compared with met...

Two trials were conducted to study the effect of multi-steps phase-feeding (PF) program on growth performance of broiler chickens from 1 to 24 and 1 to 39 d of age. The control group was the nutrient recommendation of Aviagen (2019) with a three-step PF program (1-10, 11-24 and 25-39 d of age). In the first trial, the control group was compared with an eight-step PF program (PF8), and in the se...