Search results for "Optimization"
showing 10 items of 2824 documents
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Iterative Methods for Pricing American Options under the Bates Model
2013
We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…
Super-fit and population size reduction in compact Differential Evolution
2011
Although Differential Evolution is an efficient and versatile optimizer, it has a wide margin of improvement. During the latest years much effort of computer scientists studying Differential Evolution has been oriented towards the improvement of the algorithmic paradigm by adding and modifying components. In particular, two modifications lead to important improvements to the original algorithmic performance. The first is the super-fit mechanism, that is the injection at the beginning of the optimization process of a solution previously improved by another algorithm. The second is the progressive reduction of the population size during the evolution of the population. Recently, the algorithm…
Synchronous R-NSGA-II: An Extended Preference-Based Evolutionary Algorithm for Multi-Objective Optimization
2015
Classical evolutionary multi-objective optimization algorithms aim at finding an approx- imation of the entire set of Pareto optimal solutions. By considering the preferences of a decision maker within evolutionary multi-objective optimization algorithms, it is possible to focus the search only on those parts of the Pareto front that satisfy his/her preferences. In this paper, an extended preference-based evolutionary algorithm has been proposed for solving multi-objective optimiza- tion problems. Here, concepts from an interactive synchronous NIMBUS method are borrowed and combined with the R-NSGA-II algorithm. The proposed synchronous R-NSGA-II algorithm uses preference information provid…
IMEX schemes for pricing options under jump–diffusion models
2014
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump-diffusion process. The schemes include the families of IMEX-midpoint, IMEX-CNAB and IMEX-BDF2 schemes. Each family is defined by a convex combination parameter [email protected]?[0,1], which divides the zeroth-order term due to the jumps between the implicit and explicit parts in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restric…
LOCAL CONTROL OF SOUND IN STOCHASTIC DOMAINS BASED ON FINITE ELEMENT MODELS
2011
A numerical method for optimizing the local control of sound in a stochastic domain is developed. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations is modeled using the finite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pressure field in the silent region are given by the solution of a quadratic optimization problem. The developed method computes a robust local noise control in the presence of randomly varying parameters such as variations in the acoustic space. Numerical examples consider the noise experienced by a vehicle driver with a varying posture. In a mod…
Can back-projection fully resolve polarity indeterminacy of independent component analysis in study of event-related potential?
2011
a b s t r a c t In the study of event-related potentials (ERPs) using independent component analysis (ICA), it is a traditional way to project the extracted ERP component back to electrodes for correcting its scaling (magnitude and polarity) indeterminacy. However, ICA tends to be locally optimized in practice, and then, the back-projection of a component estimated by the ICA can possibly not fully correct its polarity at every electrode. We demonstrate this phenomenon from the view of the theoretical analysis and numerical simulations and suggest checking and modifying the abnormal polarity of the projected component in the electrode field before further analysis. Moreover, when several co…
Justification of point electrode models in electrical impedance tomography
2011
The most accurate model for real-life electrical impedance tomography is the complete electrode model, which takes into account electrode shapes and (usually unknown) contact impedances at electrode-object interfaces. When the electrodes are small, however, it is tempting to formally replace them by point sources. This simplifies the model considerably and completely eliminates the effect of contact impedance. In this work we rigorously justify such a point electrode model for the important case of having difference measurements ("relative data") as data for the reconstruction problem. We do this by deriving the asymptotic limit of the complete model for vanishing electrode size. This is s…
Bilevel heat exchanger network synthesis with an interactive multi-objective optimization method
2012
Abstract Heat exchanger network synthesis (HENS) has been an active research area for more than 40 years because well-designed heat exchanger networks enable heat recovery in process industries in an energy- and cost-efficient manner. Due to ever increasing global competition and need to decrease the harmful effects done on the environment, there still is a continuous need to improve the heat exchanger networks and their synthesizing methods. In this work we present a HENS method that combines an interactive multi-objective optimization method with a simultaneous bilevel HENS method, where the bilevel part of the method is based on grouping of process streams and building aggregate streams …
Interpreting wind damage risk-how multifunctional forest management impacts standing timber at risk of wind felling
2022
AbstractLandscape multifunctionality, a widely accepted challenge for boreal forests, aims to simultaneously provide timber, non-timber ecosystem services, and shelter for biodiversity. However, multifunctionality requires the use of novel forest management regimes optimally combined over the landscape, and an increased share of sets asides. It remains unclear how this combination will shape stand vulnerability to wind disturbances and exposed timber volume. We combined forest growth simulations and multi-objective optimization to create alternative landscape level forest management scenarios. Management choices were restricted to 1) rotation forestry, 2) continuous cover forestry, and 3) a…