In insurance mathematics, optimal control problems over an infinite time horizon arise when computing risk measures. An example of such a risk measure is the expected discounted future dividend payments. In models which take multiple economic factors into account, this problem is...

This book provides a rigorous introduction to the theory, computation, and applications of variational inequalities (VIs), with a focus on applications in management science and finance. It aims to bridge the gap between the abstract mathematical treatments of the subject and simplistic,...

Intro -- Contents -- Preface -- Contributors -- Introduction -- Risk Management and Portfolio Optimization -- Importance Sampling and StratiEcation for Value-at-Risk -- ConEdence Intervals and Hypothesis Testing for the -- Sharpe and Treynor Performance Measures: -- A Bootstrap Approach --...

We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of...

Neural Control (NC) is a growing field in stochastic optimal control applied to various dynamical systems such as quadcopter. NC is a non-parametric, learning based computational scheme, capable of handling high dimensional control problems. In this paper, “NC” principles have been applied...

We present efficient partial differential equation (PDE) methods for continuous time mean-variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. The standard formulation of mean-variance optimal portfolio allocation problems, where the total wealth is...