In dieser Arbeit entwickeln wir neue Methoden und Verfahren, um aktuelle Modellierungsverfahren zu ergänzen und zu verbessern und um so ein tieferes Verständnis von Energiemärkten zu gewinnen. Wir untersuchen verschiedene Aspekte der stochastischen Modellierung von Energiemärkten: wir...

In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modifcation of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy,...

In this paper we investigate the use of finite difference and finite element schemes when applied to the valuation of exotic options characterized by discontinuities in the payoff function. In particular, we will conduct a numerical analysis of several common schemes in order to give a better...

Recent results for pricing American options based on Mellin transforms are used to derive several approximations for the critical stock price of a finite-living American option. We prove important theoretical properties of the derived approximations and compare our results to other approaches...

We apply numerical dynamic programming to multi-asset dynamic portfolio optimization problems with proportional transaction costs. Examples include problems with one safe asset plus two to six risky stocks, and seven to 360 trading periods in a finite horizon problem. These examples show that it...

Under the local volatility model, the convergence of Monte-Carlo with Milstein discretization and Euler discretization are compared for the pricing of Vanilla, Digital, discrete Barrier options as well as a more exotic variety of option, the Accumulator. A finite difference approach is also...

This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions...

The Kalman filter (KF) dates back to 1960, when R. E. Kalman provided a recursive algorithm to compute the solution of a (linear) data filtering and prediction problem, proving to be much more efficient than the N. Wiener's approach, introduced in 1949.Data filtering is a simple example of Data...

I introduce and evaluate a new stochastic simulation method for dynamic economic models. It is based on recent work in the operations research and engineering literatures (Van Roy et. al, 1997; Powell, 2007; Bertsekas, 2011). The baseline method involves rewriting the household's dynamic program in...