Abstract We analyze the errors arising from discrete rebalancing of the hedging portfolio in exponential Lévy models, and establish the rates at which the expected squared discretization error goes to zero when the length of the rebalancing step decreases. Different hedging strategies and option pay-offs are considered. The case of digital options is studied in detail, and it turns out that in ...

The residual variance estimation problem is well-known in statistics and machine learning with many applications for example in the field of nonlinear modelling. In this paper, we show that the problem can be formulated in a general supervised learning context. Emphasis is on two widely used non-parametric techniques known as the Delta test and the Gamma test. Under some regularity assumptions,...

We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a “power-law” decay around the origin and a “strongly” ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with line...

We study the detailed convergence of the binomial tree scheme. It is known that the scheme is first order. We find the exact constants, and show it is possible to modify Richardson extrapolation to get a method of order three-halves. We see that the delta, used in hedging, converges at the same rate. We analyze this by first embedding the tree scheme in the Black-Scholes diffusion model by mean...

It is demonstr ated th at the chaotic properties of neural networks (in this case networks defined by the generalized delta procedur e) can be used to improve th eir learning performance. By adapt ively varying the learning-rate parameter an annealing mechanism can be introduced that is founded in chaos. T he prop osed mechanism, chaos-based learning, provides faster convergence than standard b...

This paper proposes an improved adaptive approach involving Bacterial Foraging Algorithm (BFA) to optimize both the amplitude and phase of the weights of a linear array of antennas for maximum array factor at any desired direction and nulls in specific directions. The Bacteria Foraging Algorithm is made adaptive using principle of adaptive delta modulation. To show the improvement in making the...

The DMP1 (Dynamic Multi-layer Perceptron 1) network training method is based upon a divide and conquer approach which builds networks in the form of binary trees, dynamically allocating nodes and layers as needed. This paper introduces the DMP1 method, and compares the preformance of DMP1 when using the standard delta rule training method for training individual nodes against the performance of...

In this paper, we compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approx...

NeuroFAST is an on-line fuzzy modeling learning algorithm, featuring high function approximation accuracy and fast convergence. It is based on a first-order Takagi-Sugeno-Kang (TSK) model, where the consequence part of each fuzzy rule is a linear equation. Structure identification is performed by a fuzzy adaptive resonance theory (ART)-like mechanism, assisted by fuzzy rule splitting and adding...

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. In this paper I further test the truncated Levy paradigm u...