Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing

The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate a more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be well-approximated by the forward-variance Bergomi model with wisely chosen weights and mean-reversion speed parameters (aBergomi), which has the Markovian property. We establish an explicit bound on the L2-error between the respective kernels of these two models, which is explicitly controlled by the number of terms in the aBergomi model. We establish and describe the affine structure of the rBergomi model, and show the convergence of the affine structure of the aBergomi model to the one of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a classical Markovian Monte Carlo simulation scheme for the aBergomi model, which we compare to the hybrid scheme of the rBergomi model.

Spin Isoenergetic Process and the Lindblad Equation

A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in time. In the Markovian approximation, the corresponding Lindbladian operators are constructed without recourse to detailed information about the coupling of the subsystem with the environment called the energy bath. The entropy production rate under the resulting Lindblad equation is shown to be positive. The leading-order expressions of the power output and work done along the isoenergetic process are obtained.

Delay announcements for call centers with hyperexponential patience modeling

Purpose The purpose of this paper is to provide delay announcements for call centers with hyperexponential patience modeling. The paper aims to employ a state-dependent Markovian approximation for informing arriving customers about anticipated delay in a real call center. Design/methodology/approach Motivated by real call center data, the patience distribution is modeled by the hyperexponential distribution and is analyzed by its realistic significance, with and without delay information. Appropriate M/M/s/r+H2 queueing model is structured, including a voice response system that is employed in practice, and a state-dependent Markovian approximation is applied for computing abandonment. Based on this approximation, a method is proposed for estimating virtual delays, and it is investigated about the problem of announcing virtual delays to customers upon their arrival. Findings There are two parts of findings from the results obtained from the case study and a numerical study of simulation comparisons. First, using an H2 distribution for the abandonment distribution is driven by an empirical study which shows its good fit to real-life call center data. Second, simulation experiments indicate that the model and approximation are reasonable, and the state-dependent Markovian approximation works very well for call centers with larger pooling. It is concluded that our approach can be applied in a voice response system of real call centers. Originality/value Many results pertain to announcing delay information, customer reactions and links to estimating hyperexponential distribution based on real data that have not been established in previous studies; however, this paper analytically characterizes these performance measures for delay announcements.

Decoherence dynamics of interacting qubits coupled to a bath of local optical phonons

We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.

OPTIMIZATION OF OVERFLOW POLICIES IN CALL CENTERS

We examine how overflow policies in a multi-skill call center should be designed to accommodate performance measures that depend on waiting time percentiles such as service level. This is done using a discrete Markovian approximation of the waiting time of the first customers waiting in line. A Markov decision chain is used to determine the optimal policy. This policy outperforms considerably the ones used most often in practice, which use a fixed threshold. The present method can be used also for other call-center models and other situations where performance is based on actual waiting times and customers are treated in a FCFS order.