NOISEQ · Towards a general noise calculus with applications to finance science and technology
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2005-02-01 → 2007-01-31
- EU contribution
- €260,245
- Participants
- 1
- Scheme
- EIF
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Results in brief
Final Activity Report Summary - NOISEQ (Towards a general noise calculus with applications to finance science and technology)
Hyperbolic equations are known to be difficult to solve. The result from year 1 gives general conditions on the noise and on the coefficients assuring the existence of a unique solution of the corresponding Stochastic partial differential equation (SPDE). Parts of the result from year 2 are related to error calculations. The Hurst index of a fractional process is, in real world problems, always a measured, and therefore inaccurate, quantity. It is never a known, specific value given in advance by theoretical reasoning. This means that when simulating a real problem using a measured Hurst index, an error is made. The result of year 2 gives an estimate of how big the error is. The numerical analysis shows that, when it comes to certain stochastic partial differential equations, the relation is exactly linear. This is important in technical applications.
Data: CORDIS, © European Union
Project objective
This proposal has its focus on developing/broadening the white noise theory with applications to financial mathematics and stochastic partial differential equations (SPDEs), to allow for non-Gaussian or even non-Levy, processes.The following five research topics will be considered.1) Solution of general hyperbolic SPDEs perturbed by fractional Brownian noise. This will add greatly to the knowledge of how an important class of dynamical systems behave in a noisy environment. Creating a stochastic LP-theory, giving information on how roughness of the noise is transferred to the solution, to aid in the computation of convergence rates for numerical methods.2) Development of numerical methods and numerical analysis for use on SPDEs perturbed by non- Gaussian noise. There are currently no methods available in this situation while the demands for practical methods from the applied scientific community are clearly seen. The results will definitely be beneficial for the scientific community involved in stochastic modelling.3) and 4) Two extensions in minimal variance hedging. Calculating the change of value of processes, perturbed by intensity processes such as the doubly stochastic Poisson process (the Cox process), requires extension of the Malliavin calculus to non-Levy processes and the use of a Clark-Haussmann-Ocone theorem for this setting which is the goal of the first part of this section. The second has a similar aim but deals with applying the Donsker's delta function to compute hedging strategies for more general contingent claims. The key results should be explicit, easy-to-use, formulas so as to avoid the imprecise and time consuming use of Monte-Car lo simulation5) Anticipating calculus. To deal with price dynamics of stocks, which are not adapted t o a given filtration (market information), it is essential to develop a calculus for non-adapted processes. An anticipative Ito formula for Levy processes has recently been proved. This will be used to study portfolios under non-adaptedness. The situation of non-adaptedness will occur e.g. if an insider hedges a portfolio.
Original text from CORDIS.
Participants
- UNIVERSITETET I OSLO · OSLOCoordinatorNorway
Links
Data: CORDIS, © European Union