Let dx(t) = y(t)dt, where y(t) is Bessel process, and let T(y, η, λ) be the first time that the y(t) process, starting from y, hits either the boundary y(t) = η or y(t) = λ. The problem of keeping the value of x(T) as small as possible is considered. By choosing various termination cost functions, large values of x(T) are increasingly penalized. The optimal control is obtained by considering the uncontrolled process and its evaluation requires the computation of the moment generating function of x(τ), as well as its mean and its probability density function, where τ is the same as T, but for the uncontrolled process.
