1. When the asset pays continuous dividend yield at the rate q, the expected rate of return of the asset is r − q under the risk neutral measure (see Chap 3 of Kwok's text for justification). Under the continuous Geometric Brownian process model, the logarithm of the asset price ratio over ∆t interval is normally distributed with mean r − q − σ 2 2 ∆t and variance σ 2 ∆t. Accordingly, the mean ...

The emergent field of probabilistic numerics has thus far lacked rigorous statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain Bayesian inverse problems, albeit problems that are non-standard. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well-defined, ...

We study classical control problems like pole assignment, stabilization, linear quadratic control and H∞ control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.