A market fix serves as a benchmark for foreign exchange (FX) execution, and is employed by many institutional investors to establish an exact reference at which execution takes place. The currently most popular FX fix is the World Market Reuters (WM/R) 4pm fix. Execution at the WM/R 4pm fix is a...

In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to...

We consider a class of discrete time stochastic control problems motivated by some financial applications. We use a pathwise stochastic control approach to provide a dual formulation of the problem. This enables us to develop a numerical technique for obtaining an estimate of the value function...

This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the...

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based)...

In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [Forsyth & Labahn, 2007], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American...

Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a fully-adapted filter that utilizes conditional...

In the second half of 2009 the world experienced an intense influenza activity. The new 2009 H1N1 virus, formerly known as the swine flu, has in only five months found its way from Mexico to a majority of the countries on the planet. The fears of a large second-wave pandemic and its potential...

Quantile and least-absolute deviations (LAD) methods are popular robust statistical methods but have not generally been applied to state filtering and sequential parameter learning. This paper introduces robust state space models whose error structure coincides with quantile estimation...

We explore the use of deep learning hierarchical models for problems in financial prediction and classification. Financial prediction problems – such as those presented in designing and pricing securities, constructing portfolios, and risk management – often involve large data sets with...