5,523 research outputs found
Computing Greeks using multilevel path simulation
We investigate the extension of the multilevel Monte Carlo method [2, 3] to the calculation of Greeks. The pathwise sensitivity analysis [5] differentiates the path evolution and effectively reduces the smoothness of the payoff. This leads to new challenges: the use of naive algorithms is often impossible because of the inapplicability of pathwise sensitivities to discontinuous payoffs.\ud
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These challenges can be addressed in three different ways: payoff smoothing using conditional expectations of the payoff before maturity [5]; an approximation of the above technique using path splitting for the final timestep [1]; the use of a hybrid combination of pathwise sensitivity and the Likelihood Ratio Method [4]. We discuss the strengths and weaknesses of these alternatives in different multilevel Monte Carlo settings
Strategy updating rules and strategy distributions in dynamical multiagent systems
In the evolutionary version of the minority game, agents update their
strategies (gene-value ) in order to improve their performance. Motivated by
recent intriguing results obtained for prize-to-fine ratios which are smaller
than unity, we explore the system's dynamics with a strategy updating rule of
the form (). We find that the strategy
distribution depends strongly on the values of the prize-to-fine ratio , the
length scale , and the type of boundary condition used. We show that
these parameters determine the amplitude and frequency of the the temporal
oscillations observed in the gene space. These regular oscillations are shown
to be the main factor which determines the strategy distribution of the
population. In addition, we find that agents characterized by
(a coin-tossing strategy) have the best chances of survival at asymptotically
long times, regardless of the value of and the boundary conditions
used.Comment: 4 pages, 7 figure
2-local triple homomorphisms on von Neumann algebras and JBW-triples
We prove that every (not necessarily linear nor continuous) 2-local triple
homomorphism from a JBW-triple into a JB-triple is linear and a triple
homomorphism. Consequently, every 2-local triple homomorphism from a von
Neumann algebra (respectively, from a JBW-algebra) into a C-algebra
(respectively, into a JB-algebra) is linear and a triple homomorphism
Local triple derivations on C*-algebras
We prove that every bounded local triple derivation on a unital C*-algebra is
a triple derivation. A similar statement is established in the category of
unital JB*-algebras.Comment: 12 pages, submitte
Efficient Coupling between Dielectric-Loaded Plasmonic and Silicon Photonic Waveguides
The realization of practical on-chip plasmonic devices will require efficient coupling of light into and out of surface plasmon waveguides over short length scales. In this letter, we report on low insertion loss for polymer-on-gold dielectric-loaded plasmonic waveguides end-coupled to silicon-on-insulator waveguides with a coupling efficiency of 79 ± 2% per transition at telecommunication wavelengths. Propagation loss is determined independently of insertion loss by measuring the transmission through plasmonic waveguides of varying length, and we find a characteristic surface-plasmon propagation length of 51 ± 4 μm at a free-space wavelength of λ = 1550 nm. We also demonstrate efficient coupling to whispering-gallery modes in plasmonic ring resonators with an average bending-loss-limited quality factor of 180 ± 8
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