The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so...

In this paper which will appear as a chapter in the Handbook ofGeneralized Convexity we discuss the basic ideas ofconvex and quasiconvex analysis in finite dimensional Euclideanspaces. To illustrate the usefulness of this branchof mathematics also applications to optimization theory...

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

This article establishes the Poisson optional stopping times (POST) method by [22] as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker is permitted to "stop", i.e. exercise the...

In this paper, we develop a new capital adequacy buffer model (CABM) which is sensitive to dynamic economic circumstances. The model, which measures additional bank capital required to compensate for fluctuating credit risk, is a novel combination of the Merton structural model which measures...