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A Visual Criterion for Identifying Ito Diffusions as Martingalesor Strict Local Martingales

Hulley, Hardy; Platen, Eckhard - Finance Discipline Group, Business School - 2009

It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as...

Persistent link: https://www.econbiz.de/10008506970

A Visual Classification of Local Martingales

Hulley, Hardy; Platen, Eckhard - Finance Discipline Group, Business School - 2008

This paper considers the problem of when a local martingale is a martingale or a universally integrable martingale, for the case of time-homogeneous scalar diffusions. Necessary and suffcient conditions of a geometric nature are obtained for answering this question. These results are widely...

Persistent link: https://www.econbiz.de/10005041733

Quasi-exact Approximation of Hidden Markov Chain Filters

Platen, Eckhard; Rendek, Renata - Finance Discipline Group, Business School - 2009

This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper...

Persistent link: https://www.econbiz.de/10008506969

On the Numerical Stability of Simulation Methods for SDES

Platen, Eckhard; Shi, Lei - Finance Discipline Group, Business School - 2008

stability is clearly more important than numerical efficiency or some higher order of convergence. Discrete time approximations … of solutions of SDEs are widely used in simulations in finance and other areas of application. The stability criterion … martingale dynamics arise for solutions of SDEs and diffusion coefficients are often of multiplicative type. Stability regions …

Persistent link: https://www.econbiz.de/10004984500

Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps

Kubilius, Kestutis; Platen, Eckhard - Finance Discipline Group, Business School - 2001

The paper estimates the speed of convergence of the Euler approximation for diffussion processes with jump component which have Holder continuous coefficients.

Persistent link: https://www.econbiz.de/10004984535

On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance

Liberati, Nicola Bruti; Platen, Eckhard - Finance Discipline Group, Business School - 2004

The purpose of this paper is to study the efficiency of simplified weak schemes for stochastic differential equations. We present a numerical comparison between weak Taylor schemes and their simplified versions. In the simplified schemes discrete random variables, instead of Gaussian ones, are...

Persistent link: https://www.econbiz.de/10004984547

Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations

Bruti-Liberati, Nicola; Platen, Eckhard - Finance Discipline Group, Business School - 2008

stability properties of the new symmetric predictor-corrector Euler methods. …

Persistent link: https://www.econbiz.de/10005041725

Applications of the Balanced Method to Stochastic Differential Equations in Filtering

Fischer, P.; Platen, Eckhard - Finance Discipline Group, Business School - 1999

The paper studies the application of the balanced method in hidden Markov chain filtering, an important practical area that requires the strong numerical solution of stochstic differential equations with multiplicative noise. Numerical experiments are conducted to enable comparisons between the...

Persistent link: https://www.econbiz.de/10005041744

Heterogeneous Beliefs and Adaptive Behaviour in a Continuous-Time Asset Price Model

He, Xue-Zhong; Li, Kai - Finance Discipline Group, Business School - 2011

heterogeneous agents and stability impact of lagged price information used by chartists to form their expectations. For the … chartists on market stability. For the stochastic model, we demonstrate that the model is able to display various market …

Persistent link: https://www.econbiz.de/10009357757

Herding, Trend Chasing and Market Volatility

Guilmi, Corrado Di; He, Xue-Zhong; Li, Kai - Finance Discipline Group, Business School - 2013

We introduce a heterogeneous agent asset pricing model in continuoustime to show that trend chasing, switching and herding all contribute to market volatility in price and return and volatility clustering, but their impact are different. On the one hand, the fluctuations of market price and...

Persistent link: https://www.econbiz.de/10010754095