arXiv subjects

Rohini Kumar

Publications and source records attributed to Rohini Kumar.

13 recordsLinked to original sources

arXiv2025

Undulating patterns of Hysteresis loops in diurnal seasonality of air temperature in Urban Heat Island effect: Insights from Paris and Madrid

This study examines the dynamics of the urban heat island (UHI) effect by conducting a comparative analysis of air temperature hysteresis patterns in Paris and Madrid, two major European cities with distinct climatic and urban characteristics. Utilizing high-resolution modelled air temperature data aggregated at a fine temporal resolution of three-hour intervals from 2008 to 2017, we investigate how diurnal and seasonal hysteresis loops reveal both unique and universal aspects of UHI variability. Paris, located in a temperate oceanic climate, and Madrid, situated in a cold semi-arid zone, display pronounced differences in UHI intensity, seasonal distribution, and diurnal patterns. Despite these contrasts, both cities exhibit remarkably similar hysteresis loop directions and slopes, suggesting that time-dependent mechanisms such as solar radiation and heat storage fundamentally govern air temperature UHI across diverse urban contexts. Our findings underscore the importance of considering both local climate and universal physical processes in developing targeted, climate-resilient urban strategies. The results pave the way for group-based interventions and classification of cities by hysteresis patterns to inform urban planning and heat mitigation efforts.

physics.soc-ph↗

arXiv2024

Risk-indifference Pricing of American-style Contingent Claims

This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time, in a setting where buyer and seller have potentially different information, and show that these definitions are consistent with no-arbitrage principles. Specifying to stochastic volatility models, we characterize indifference prices via solutions of Backward Stochastic Differential Equations reflected at Backward Stochastic Differential Equations and show that this characterization provides a basis for the implementation of numerical methods using deep learning.

q-fin.PR↗

arXiv2023

Contemporary climate analogs project north-south polarization of urban water-energy nexus across US cities under warming climate

Despite the coupled nature of water and electricity demand, the two utilities are often managed by different entities with minimal interaction. Neglecting the water-energy demand nexus leads to to suboptimal management decisions, particularly under climate change. Here, we leverage state-of-the-art machine learning and contemporary climate analogs to project the city-level coupled water and electricity demand of 46 major U.S. cities into the future. The results show that many U.S. cities may experience an increase in electricity (water) demand of up to 20% (15%) due to climate change under a high emissions scenario, with a clear north-south gradient. In the absence of appropriate mitigation strategies, these changes will likely stress current infrastructure, limiting the effectiveness of the ongoing grid decarbonization efforts. In the event that cities are unable to match the increasing demand, there may be increased occurrence of supply shortages, leading to blackouts with disproportionate impacts on vulnerable populations. As such, reliable projections of future water and electricity demand under climate change are critical not only for preventing further exacerbation of the existing environmental injustices but also for more effective design and execution of climate change mitigation and adaptation plans.

stat.AP↗

arXiv2022

On the evolution of agricultural and non-agricultural produce flow network in India

Rising economic instability and continuous evolution in international relations demand a self-reliant trade and commodity flow networks at regional scales to efficiently address the growing human needs of a nation. Despite its importance in securing India's food security, the potential advantages of inland trade remain unexplored. Here we perform a comprehensive analysis of agricultural flows and contrast it with non-agricultural commodities flow across Indian states. The spatiotemporal evolution of both the networks for the period 2010 to 2018 was studied and compared using network properties along with the total traded value. Our results show an increase in annual traded volume by nearly 37 % and 87 %, respectively, for agriculture and non-agriculture trade. An increase in total trade volume without a significant increase in connectivity over the analyzed time-period is observed in both networks, reveals the over-reliance and increased dependency on particular export hubs. Our analysis further revealed a more homogeneous distribution between import and export connection nodes for agriculture trade compared to non-agriculture trade, where Indian states with high exports also have high imports. Overall our analysis provide a quantitative description of Indian inland trade as a complex network that could further us design resilient trade networks within the nation.

physics.soc-ph↗

arXiv2019

Integrated analysis of the urban water-electricity demand nexus in the Midwestern United States

Considering the interdependencies between water and electricity use is critical for ensuring conservation measures are successful in lowering the net water and electricity use in a city. This water-electricity demand nexus will become even more important as cities continue to grow, causing water and electricity utilities additional stress, especially given the likely impacts of future global climatic and socioeconomic changes. Here, we propose a modeling framework based in statistical learning theory for predicting the climate-sensitive portion of the coupled water-electricity demand nexus. The predictive models were built and tested on six Midwestern cities. The results showed that water use was better predicted than electricity use, indicating that water use is slightly more sensitive to climate than electricity use. Additionally, the results demonstrated the importance of the variability in the El Nino/Southern Oscillation index, which explained the majority of the covariance in the water-electricity nexus. Our modeling results suggest that stronger El Ninos lead to an overall increase in water and electricity use in these cities. The integrated modeling framework presented here can be used to characterize the climate-related sensitivity of the water-electricity demand nexus, accounting for the coupled water and electricity use rather than modeling them separately, as independent variables.

cs.LG↗

arXiv2016

Asymptotic approximation of optimal portfolio for small time horizons

We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form formula for a trading strategy which approximates the optimal trading strategy when the time horizon is small. This strategy is generated by a first order approximation to the value function. The approximate value function is obtained by constructing classical sub- and super-solutions to the HJB PDE using a formal expansion in powers of horizon time. Martingale inequalities are used to sandwich the true value function between the constructed sub- and super-solutions. A rigorous proof of the accuracy of the approximation formulas is given. We end with a heuristic scheme for extending our small-time approximating formulas to approximating formulas in a finite time horizon.

math.PR↗

arXiv2015

Large deviations for multi-scale jump-diffusion processes

We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our results extend previous large deviation results for diffusions. We provide concrete examples in their applications to finance and biology, with an explicit calculation of the large deviation rate function.

math.PR↗

arXiv2015

Effect of Volatility Clustering on Indifference Pricing of Options by Convex Risk Measures

In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indifference price in their article is obtained by using dynamic convex risk measures given by backward stochastic differential equations. Volatility clustering is modelled by a fast mean-reverting volatility in a stochastic volatility model for stock price. Asymptotics of the indifference price of options and their corresponding implied volatility are obtained in this article, as the mean-reversion time approaches zero. Correction terms to the asymptotic option price and implied volatility are also obtained.

q-fin.MF↗

arXiv2014

Large deviations for the boundary local time of doubly reflected Brownian Motion

We compute a closed-form expression for the moment generating function $\hat{f}(x;\lambda,\alpha)=\frac{1}{\lambda}\mathbb{E}_x(e^{\alpha L_{\tau}})$, where $L_t$ is the local time at zero for standard Brownian motion with reflecting barriers at $0$ and $b$, and $\tau \sim \mathrm{Exp}(\lambda)$ is independent of $W$. By analyzing how and where $\hat{f}(x;\cdot,\alpha)$ blows up in $\lambda$, a large-time large deviation principle (LDP) for $L_t/t$ is established using a Tauberian result and the G\"{a}rtner-Ellis Theorem.

math.PR↗

arXiv2010

Current fluctuations for independent random walks in multiple dimensions

Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random walks. Consider a box centered around an observer who starts at the origin and moves with constant velocity $\vec{v}$. To observe interesting fluctuations beyond the translation of initial density fluctuations, we measure the net flux of particles over time into this moving box. We call this the ``box-current" process. We generalize this current process to a distribution valued process. Scaling time by $n$ and space by $\sqrt{n}$ gives current fluctuations of order $n^{d/4}$ where $d$ is the space dimension. The scaling limit of the normalized current process is a distribution valued Gaussian process with given covariance. The limiting current process is equal in distribution to the solution of a given stochastic partial differential equation which is related to the generalized Ornstein-Uhlenbeck process.

math.PR↗

arXiv2010

Small-time asymptotics for fast mean-reverting stochastic volatility models

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce asymptotic prices for out-of-the-money call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in Feng, Forde and Fouque [SIAM J. Financial Math. 1 (2010) 126-141] by a moment generating function computation in the particular case of the Heston model.

q-fin.PR↗

arXiv2010

TASEP with Discontinuous Jump Rates

We prove a hydrodynamic limit for the totally asymmetric simple exclusion process with spatially inhomogeneous jump rates given by a speed function that may admit discontinuities. The limiting density profiles are described with a variational formula. This formula enables us to compute explicit density profiles even though we have no information about the invariant distributions of the process. In the case of a two-phase flow for which a suitable p.d.e. theory has been developed we also observe that the limit profiles are entropy solutions of the corresponding scalar conservation law with a discontinuous speed function.

math.PR↗

arXiv2008

Space-Time Current Process for Independent Random Walks in One Dimension

In a system made up of independent random walks, fluctuations of order $n^{1/4}$ from the hydrodynamic limit come from particle current across characteristics. We show that a two-parameter space-time particle current process converges to a two-parameter Gaussian process. These Gaussian processes also appear as the limit for the one-dimensional random average process. The final section of this paper looks at large deviations of the current process.

math.PR↗