Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.

Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

This paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment

This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently consider a regime in which the claim arrival intensity and transition rates of the environmental process are jointly sped up, and one in which there is (with overwhelming probability) maximally one transition of the environmental process in the time interval considered. The approximations are extensively tested in a series of numerical experiments.

Comprehensive analysis of elevator static sectoring control systems using Monte Carlo simulation

For a long time, there was no action that a group controller could take during incoming traffic conditions other than returning the elevators back to the main entrance and opening their doors. Passengers would arrive in the main entrance and board the first available elevator car. However, in the early 1990s, sectoring was introduced during incoming traffic conditions. Sectoring is the soft division of the building into groups of (usually but not necessarily contiguous) floors, usually of equal populations. One or more elevators are assigned to a sector. The allocation of the elevator(s) to a sector can either be fixed (static sectoring) or variable (dynamic sectoring) within consecutive round trips. In addition, the size and composition of the different sectors can be static or dynamic. Sectoring is thus a powerful tool in dealing with peaks of incoming traffic demand. However, most of the analysis carried out to understand the effects of sectoring on the performance of the elevator traffic system has been based on simulation only. This paper presents a comprehensive calculation-based analysis of static sectoring control for incoming traffic as a control tool. The analysis is based on the approach of progressively increasing the number of sectors in a building, starting from a single sector (i.e., no sectoring) and proceeding to full sectoring (where the number of sectors equals the number of elevators in the group) and even increasing the number of sectors up to the total number of floors above the main entrance (which has been given the new term: super-sectoring). An analysis is carried out in each case showing the handling capacity, car loading, average waiting time, and average traveling time. Practical application: This paper allows a control system designer to adapt the actions of the controller to the change in passenger arrivals. The control can detect the intensity of passenger arrivals and adjust the number of sectors to suit such an arrival intensity. The aim would be to maximize the handling capacity of the system or minimize the car loading.

Subordinated Binomial Option Pricing with Stochastic Arrival Intensity and Untraded Underlying Asset

We extend the subordinated binomial option pricing model with stochastic arrival intensity (Chang, Chang and Lu, 2010) to allow for untraded underlying assets by using matching futures prices to imply out the underlying asset values. We empirically apply the model to VIX option pricing vis-à-vis the original model with constant arrival intensity (Chang, Chang and Tian, 2006) using a two-year set of daily VIX options and futures data to specifically examine the efficacy of adding stochastic arrival intensity and untraded underlying assets. We find that the extended version significantly outperforms the original model both in sample and out-of-sample in terms of the MSE, with pricing error reduction about 37% and 32%, respectively, and additionally the outperformance is robust to the selection of the constant arrival intensity level. We attribute the outperformance to the extended model’s incorporation of the stylized effects of mean-reversion and clustering in intensity arrivals as well as of the information content conveyed by the matching futures prices.

A regime-switching model with jumps and its application to bond pricing and insurance

In this paper, we consider a Markovian, regime-switching model with jumps and its application to bond pricing and insurance. The jumps in the model are described by a compound Cox process, where the arrival intensity of the counting number-process follows a regime-switching shot noise process. Using a martingale method, we derive exponential-affine form expressions for the price of a zero-coupon bond and the joint Laplace transform of the aggregate accumulated claims and the arrival intensity.

Poisson hail on a hot ground

We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACSs) of the Euclidean space. These RACSs arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling on the Euclidean plane, this is the height of the hailstone, whereas the RACS is its footprint). The Euclidean space serves customers at speed 1. The service discipline is a hard exclusion rule: no two intersecting RACSs can be served simultaneously and service is in the first-in–first-out order, i.e. only the hailstones in contact with the ground melt at speed 1, whereas the others are queued. A tagged RACS waits until all RACSs that arrived before it and intersecting it have fully melted before starting its own melting. We give the evolution equations for this queue. We prove that it is stable for a sufficiently small arrival intensity, provided that the typical diameter of the RACS and the typical service time have finite exponential moments. We also discuss the percolation properties of the stationary regime of the RACS in the queue.

Poisson hail on a hot ground

We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACSs) of the Euclidean space. These RACSs arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling on the Euclidean plane, this is the height of the hailstone, whereas the RACS is its footprint). The Euclidean space serves customers at speed 1. The service discipline is a hard exclusion rule: no two intersecting RACSs can be served simultaneously and service is in the first-in–first-out order, i.e. only the hailstones in contact with the ground melt at speed 1, whereas the others are queued. A tagged RACS waits until all RACSs that arrived before it and intersecting it have fully melted before starting its own melting. We give the evolution equations for this queue. We prove that it is stable for a sufficiently small arrival intensity, provided that the typical diameter of the RACS and the typical service time have finite exponential moments. We also discuss the percolation properties of the stationary regime of the RACS in the queue.