Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

Disentangling stochastic signals superposed on short localized oscillations

We introduce a procedure for separating periodic oscillations superposed on a stochastic signal. The procedure combines empirical mode decomposition (EMD) of a signal with tools of data analysis based on stochastic differential equations, namely nonlinear Langevin equations. Taking the set of modes retrieved from the EMD of the signal, our procedure is able to separate them into two groups, one composing the periodic signal and another composing the stochastic signal. The framework is robust for a broad family of localized oscillations, in the range of large frequencies. In particular, we show that, in this context, the EMD method outperforms a low-pass filter and is robust for a wide interval of different frequency ranges and amplitudes of the periodic oscillation, as well as for a broad family of different non-linear Langevin processes.     

On stochastic auctions in risk-averse electricity markets with uncertain supply

This paper studies risk in a stochastic auction which facilitates the integration of renewable generation in electricity markets. We model market participants who are risk averse and reflect their risk aversion through coherent risk measures. We uncover a closed form characterization of a risk-averse generator’s optimal pre-commitment behaviour for a given real-time policy, both with and without risk trading.     

Power-of-two sampling in redundancy systems: The impact of assignment constraints

A classical sampling strategy for load balancing policies is power-of-two, where any server pair is sampled with equal probability. This does not cover practical settings with assignment constraints which force non-uniform sampling. While intuition suggests that non-uniform sampling adversely impacts performance, this was only supported through simulations, and rigorous statements have remained elusive. Building on product-form distributions for redundancy systems, we prove the stochastic dominance of uniform sampling for a four-server system as well as arbitrary-size systems in light traffic.     

Analyzing the coexistence of DSRC and Wi-Fi networks using the Poisson line Cox process

Vehicular networks can aid in traffic monitoring, autonomous driving, and car accidents prevention. Yet, the deployment of these networks has been delayed due to the limited spectrum, especially for the case of unlicensed operations. To handle this issue, the Federal Communications Commission (FCC) proposed to permit Wi-Fi devices to operate in the 5.9 GHz band allocated to the intelligent transportation system (ITS). In a recent work, we analyzed the impact of the coexistence of dedicated short range communications (DSRC) and Wi-Fi on future DSRC network deployments by developing a stochastic geometry analytical model that considers a dynamic medium access probability (MAP) of DSRC nodes which uses carrier sense multiple access with collision avoidance (CSMA/CA). This previous work was based on the standard 2D homogeneous Poisson Point Process (PPP) model. In this work, we model the roads using the more applicable but more complex Poisson line process (PLP) Cox point process. We generate performance metrics represented through coverage probability and area system throughput, and we compare these results to our earlier work. The importance of this work is two-fold. First, it allows a further understanding of the impact of DSRC-Wi-Fi coexistence on future DSRC network deployments, and second, it highlights the effectiveness of the PLP in modeling the distribution of vehicles in an area by producing more accurate performance results.