16,792 research outputs found
Measuring kinetic energy changes in the mesoscale with low acquisition rates
We describe a new technique to estimate the mean square velocity of a
Brownian particle from time series of the position of the particle sampled at
frequencies several orders of magnitude smaller than the momentum relaxation
frequency. We apply our technique to determine the mean square velocity of
single optically trapped polystyrene microspheres immersed in water. The
velocity is increased applying a noisy electric field that mimics a higher
kinetic temperature. Therefore, we are able to measure the average kinetic
energy change in isothermal and non-isothermal quasistatic processes. Moreover,
we show that the dependence of the mean square time-averaged velocity on the
sampling frequency can be used to quantify properties of the electrophoretic
mobility of a charged colloid. Our method could be applied to detect
temperature gradients in inhomogeneous media and to characterize the complete
thermodynamics of microscopic heat engines.Comment: 9 pages, 5 figure
Optimality of linearity with collusion and renegotiation
This study analyzes a continuous-time N-agent Brownian hidden-action model with exponential utilities, in which agents' actions jointly determine the mean and the variance of the outcome process. In order to give a theoretical justification for the use of linear contracts, as in Holmstrom and Milgrom (1987), we consider a variant of its generalization given by Sung (1995), into which collusion and renegotiation possibilities among agents are incorporated. In this model, we prove that there exists a linear and stationary optimal compensation scheme which is also immune to collusion and renegotiation
Zooming in on Quantum Trajectories
We propose to use the effect of measurements instead of their number to study
the time evolution of quantum systems under monitoring. This time redefinition
acts like a microscope which blows up the inner details of seemingly
instantaneous transitions like quantum jumps. In the simple example of a
continuously monitored qubit coupled to a heat bath, we show that this
procedure provides well defined and simple evolution equations in an otherwise
singular strong monitoring limit. We show that there exists anomalous
observable localised on sharp transitions which can only be resolved with our
new effective time. We apply our simplified description to study the
competition between information extraction and dissipation in the evolution of
the linear entropy. Finally, we show that the evolution of the new time as a
function of the real time is closely related to a stable Levy process of index
1/2.Comment: 5 pages, 2 figure
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio
We use a continuous version of the standard deviation premium principle for
pricing in incomplete equity markets by assuming that the investor issuing an
unhedgeable derivative security requires compensation for this risk in the form
of a pre-specified instantaneous Sharpe ratio. First, we apply our method to
price options on non-traded assets for which there is a traded asset that is
correlated to the non-traded asset. Our main contribution to this particular
problem is to show that our seller/buyer prices are the upper/lower good deal
bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko
(2006) and to determine the analytical properties of these prices. Second, we
apply our method to price options in the presence of stochastic volatility. Our
main contribution to this problem is to show that the instantaneous Sharpe
ratio, an integral ingredient in our methodology, is the negative of the market
price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar
(2000).Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe
ratio, correlated assets, stochastic volatility, non-linear partial
differential equations, good deal bound
Coupling iterated Kolmogorov diffusions
The Kolmogorov (1934) diffusion is the two-dimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals integral integral B d s d t,... as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals
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