The geometric Brownian motion is the solution of a linear stochastic differential equation in the Itô-sense. If one adds to the drift term a possible nonlinear time delayed term and starts with a nonnegative initial process then the process generated in this way, may hit zero and may oscillate...

This paper studies the oscillatory properties of solutions of linear scalar stochastic delay differential equations with multiplicative noise. It is shown that such noise will induce an oscillation in the solution whenever there is negative feedback from the delay term. The zeros of the process...

Assume L is a non-deterministic real valued Lévy process and f is a smooth function on [0,t]

Die Berechnung des VaR führt zur Reduktion der Dimension des Raumes der Risikofaktoren. Die vorzunehmenden Vereinfachungen resultieren aus unterschiedlichen Beweggründen, z.B. technische Effizienz, Sachlogik der Ergebnisse und statistische Adäquanz des Modells. Im Kapitel 2 stellen wir drei...

This paper gives a selective review on the recent developments of nonparametric methods in continuous-time finance, particularly in the areas of nonparametric estimation of diffusion processes, nonparametric testing of parametric diffusion models, and nonparametric pricing of derivatives. For...

We consider the problem of strong approximations of the solution of stochastic functional differential equations of Itô form with a distributed delay term in the drift and diffusion coefficient. We provide necessary background material, and give convergence proofs for the Euler-Maruyama and the...

We introduce an easy way of analyzing the transitional dynamics of the Uzawa-Lucas endogenous growth model. We use the value function approach to solve both the social planner?s optimization problem and the representative agent?s optimization problem in the decentralized economy. The complexity...

Stochastic delay differential equations (SDDEs for short) appear naturally in the description of many processes, e.g. in population dynamics with a time lag due to an age-dependent birth rate (Scheutzow 1981), in economics where a certain "time to build" is needed (Kydland and Prescott 1982) or...