An unsupervised deep learning approach in solving partial integro-differential equations

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep learning, pre-calculated labels are used to train neural networks to fit the solution of the PIDE. In an unsupervised deep learning, neural networks are employed as the solution, and the derivatives and the integrals in the PIDE are calculated based on the neural network. By matching the PIDE and its boundary conditions, the neural network gives an accurate solution of the PIDE. Once trained, it would be fast for calculating options values as well as option Greeks.Comment: 22 pages, 4 figure

A fast method for pricing American options under the variance gamma model

We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference method and the simulation method can be used for pricing under this model, but their speed is not satisfactory. So there is a need for fast but accurate approximation methods. In the case of Black-Merton-Scholes model, there are fast approximation methods, but they cannot be utilized for the variance gamma model. We develop a new fast method inspired by the quadratic approximation method, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our proposed method with those of the existing methods and show that this method is efficient and accurate for practical use.Comment: 16 pages, 1 Figure, 4 Table

Equitable Optimization of Patient Re-allocation and Temporary Facility Placement to Maximize Critical Care System Resilience in Disasters

End-stage renal disease patients face a complicated sociomedical situation and rely on various forms of infrastructure for life-sustaining treatment. Disruption of these infrastructures during disasters poses a major threat to their lives. To improve patient access to dialysis treatment, there is a need to assess the potential threat to critical care facilities from hazardous events. In this study, we propose optimization models to solve critical care system resilience problems including patient and medical resource allocation. We use human mobility data in the context of Harris County (Texas) to assess patient access to critical care facilities, dialysis centers in this study, under the simulated hazard impacts, and we propose models for patient re-allocation and temporary medical facility placement to improve critical care system resilience in an equitable manner. The results show (1) the capability of the optimization model in efficient patient re-allocation to alleviate disrupted access to dialysis facilities; (2) the importance of large facilities in maintaining the functioning of the system. The critical care system, particularly the network of dialysis centers, is heavily reliant on a few larger facilities, making it susceptible to targeted disruption. (3) The consideration of equity in the optimization model formulation reduces access loss for vulnerable populations in the simulated scenarios. (4) The proposed temporary facilities placement could improve access for the vulnerable population, thereby improving the equity of access to critical care facilities in disaster. The proposed patient re-allocation model and temporary facilities placement can serve as a data-driven and analytic-based decision support tool for public health and emergency management plans to reduce the loss of access and disrupted access to critical care facilities and would reduce the dire social costs.Comment: 21 pages, 9 figure

Network Diffusion Model Reveals Recovery Multipliers and Heterogeneous Spatial Effects in Post-Disaster Community Recovery

Community recovery from hazards and crises occurs through various diffusion processes within social and spatial networks of communities. Existing knowledge regarding the diffusion of recovery in community socio-spatial networks, however, is rather limited. To bridge this gap, in this study, we created a network diffusion model to characterize the unfolding of population activity recovery in spatial networks of communities. Using data related to population activity recovery durations calculated from location-based data in the context of 2017 Hurricane Harvey in the Houston area, we parameterized the threshold-based network diffusion model and evaluated the extent of homogeneity in spatial effects. Then we implemented the network diffusion model along with the genetic algorithm to simulate and identify recovery multipliers. The results show that the spatial effects of recovery are rather heterogeneous across spatial areas; some spatial areas demonstrate a greater spatial effect (spatial interdependence) in their recovery compared with others. Also, the results show that low-income areas demonstrate a greater spatial effect in their recovery. The greater spatial effects in recovery of low-income areas imply more reliance on resources and facilities of neighboring areas and also explain the existence of slow recovery hotspots in areas where socially vulnerable populations reside. Also, the results show that low-income and minority areas are community recovery multipliers; the faster the recovery of these recovery multipliers; the faster the recovery of the entire community. Hence, prioritizing these areas for recovery resource allocation could expedite the recovery of the overall community and promote recovery equality and equity.Comment: 20 pages, 9 figures, 2 table

Hazard Exposure Heterophily: A Latent Characteristic in Socio-Spatial Networks Influencing Community Resilience

We present a latent characteristic in socio-spatial networks, hazard-exposure heterophily, to capture the extent to which populations with similar hazard exposure could assist each other through social ties. Heterophily is the tendency of unlike individuals to form social ties. Conversely, populations in spatial areas with significant hazard exposure similarity, homophily, would lack sufficient resourcefulness to aid each other to lessen the impact of hazards. In the context of the Houston metropolitan area, we use Meta's Social Connectedness data to construct a socio-spatial network in juxtaposition with flood exposure data from National Flood Hazard Layer to analyze flood hazard exposure of spatial areas. The results reveal the extent and spatial variation of hazard-exposure heterophily in the study area. Notably, the results show that lower-income areas have lower hazard-exposure heterophily possibly caused by income segregation and the tendency of affordable housing development to be located in flood zones. Less resourceful social ties due to high hazard-exposure homophily may inhibit low-income areas from better coping with hazard impacts and could contribute to their slower recovery. Overall, the results underscore the significance of characterizing hazard-exposure heterophily in socio-spatial networks to reveal community vulnerability and resilience to hazards.Comment: 14 pages, 6 figure

A New Iterative Elliptic PDE Solver On A Distributed Pc Cluster.

Advancement in parallel computers technology has greatly influenced the numerical methods used for solving partial differential equations (pdes). A lot of attention has been devoted to the development of .numerical schemes which are suitable for the parallel environment