Corporate credit risk prediction under stochastic volatility and jumps

This paper examines the impact of allowing for stochastic volatility and jumps (SVJ) in a structural model on corporate credit risk prediction. The results from a simulation study verify the better performance of the SVJ model compared with the commonly used Merton model, and three sources are provided to explain the superiority. The empirical analysis on two real samples further ascertains the importance of recognizing the stochastic volatility and jumps by showing that the SVJ model decreases bias in spread prediction from the Merton model, and better explains the time variation in actual CDS spreads. The improvements are found particularly apparent in small firms or when the market is turbulent such as the recent financial crisis.

Stochastic output feedback model predictive control

This paper addresses the issue of output feedback model predictive control for linear systems with input constraints and stochastic disturbances. We show that the optimal policy uses the Kalman filter for state estimation, but the resultant state estimates are not utilized in a certainty equivalence control law

Stochastic ranking method for thermostatically controllable appliances to provide regulation services

Demand response can be used for providing regulation services in the electricity markets. The retailers can bid in a day-ahead market and respond to real-time regulation signal by load control. This paper proposes a new stochastic ranking method to provide regulation services via demand response. A pool of thermostatically controllable appliances (TCAs) such as air conditioners and water heaters are adjusted using direct load control method. The selection of appliances is based on a probabilistic ranking technique utilizing attributes such as temperature variation and statuses of TCAs. These attributes are stochastically forecasted for the next time step using day-ahead information. System performance is analyzed with a sample regulation signal. Network capability to provide regulation services under various seasons is analyzed. The effect of network size on the regulation services is also investigated.

Stochastic analysis of transit route segments' passenger load variation for capacity and quality of service assessment

This paper investigates stochastic analysis of transit segment hourly passenger load factor variation for transit capacity and quality of service (QoS) analysis using Automatic Fare Collection data for a premium radial bus route in Brisbane, Australia. It compares stochastic analysis to traditional peak hour factor (PHF) analysis to gain further insight into variability of transit route segments’ passenger loading during a study hour. It demonstrates that hourly design load factor is a useful method of modeling a route segment’s capacity and QoS time history across the study weekday. This analysis method is readily adaptable to different passenger load standards by adjusting design percentile, reflecting either a more relaxed or more stringent condition. This paper also considers hourly coefficient of variation of load factor as a capacity and QoS assessment measure, in particular through its relationships with hourly average and design load factors. Smaller value reflects uniform passenger loading, which is generally indicative of well dispersed passenger boarding demands and good schedule maintenance. Conversely, higher value may be indicative of pulsed or uneven passenger boarding demands, poor schedule maintenance, and/or bus bunching. An assessment table based on hourly coefficient of variation of load factor is developed and applied to this case study. Inferences are drawn for a selection of study hours across the weekday studied.

Stochastic analysis of transit route segments' passenger load variation for capacity & quality of service assessment

This study uses weekday Automatic Fare Collection (AFC) data on a premium bus line in Brisbane, Australia •Stochastic analysis is compared to peak hour factor (PHF) analysis for insight into passenger loading variability •Hourly design load factor (e.g. 88th percentile) is found to be a useful method of modeling a segment’s passenger demand time-history across a study weekday, for capacity and QoS assessment •Hourly coefficient of variation of load factor is found to be a useful QoS and operational assessment measure, particularly through its relationship with hourly average load factor, and with design load factor •An assessment table based on hourly coefficient of variation of load factor is developed from the case study

Multi-action recognition via stochastic modelling of optical flow and gradients

In this paper we propose a novel approach to multi-action recognition that performs joint segmentation and classification. This approach models each action using a Gaussian mixture using robust low-dimensional action features. Segmentation is achieved by performing classification on overlapping temporal windows, which are then merged to produce the final result. This approach is considerably less complicated than previous methods which use dynamic programming or computationally expensive hidden Markov models (HMMs). Initial experiments on a stitched version of the KTH dataset show that the proposed approach achieves an accuracy of 78.3%, outperforming a recent HMM-based approach which obtained 71.2%.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.