Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

Weak and strong Taylor methods for numerical solutions of stochastic differential equations

We apply the results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we determine weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to find precise and quick algorithms. In contrast to methods such as Euler-Maruyama-Monte-Carlo for the full SDE, we obtain more tractable expressions for accurate pricing. In particular, we present a readily tractable alternative to 'freezing the drift' in LIBOR market models that has an accuracy similar to the Euler-Maruyama-Monte-Carlo scheme for the full LIBOR market model. Numerical examples underline our results.Stochastic volatility, LIBOR market models, Mathematical finance, Option pricing via simulation, Interest rate modelling, Interest rate derivatives, Malliavin calculus,

Human trafficking in Greece

Greece has been both a destination and a transit country for human trafficking since the 1990s. Public perceptions, the understanding and policy responses towards trafficking have been shaped by its connection with migration and the conditions of migrant exploitation in various sectors of the Greek economy. Using the rubric of criminogenic asymmetries to bring the above dimensions fully into the analysis, this chapter builds on extant research and other open sources to offer an overview of the issue of trafficking and the development of policy responses in Greece