arXiv subjects

Srikanth Iyer

Publications and source records attributed to Srikanth Iyer.

6 recordsLinked to original sources

arXiv2026

Flocking by stopping: a novel mechanism of emergent order in collective movement

Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors, resulting in ordered movement. In small flocks, noise induced order can also emerge with individuals copying only a randomly chosen single neighbor at a time. We propose a new model of collective movement, inspired by how real animals move, where individuals can move in two directions or remain stationary. We demonstrate that when individuals interact with a single neighbor through a novel form of halting interaction -- where an individual may stop upon encountering an oppositely moving neighbor rather than instantly aligning -- persistent collective order can emerge even in large populations. This represents a fundamentally different mechanism from conventional averaging-based or noise-induced ordering. Using deterministic and stochastic mean-field approximations, we characterize the conditions under which such ``flocking by stopping'' behavior can occur, and confirm the mean-field predictions using individual-based simulations. Our results highlight how incorporating a stopped state and halting interactions can generate new routes to order in collective movement.

q-bio.QM↗

arXiv2025

Robust Hedging of path-dependent options using a min-max algorithm

We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$. We propose a model-free approach to construct such a portfolio. The framework is inspired by the \textit{primal-dual} Martingale Optimal Transport (MOT) problem, which was pioneered by \cite{beiglbock2013model}. The optimization problem is to determine the portfolio composition that minimizes the expected worst-case hedging error at $t_1$ (that coincides with the maturity of the options that are used in the hedging portfolio). The worst-case scenario corresponds to the distribution that yields the worst possible hedging performance. This formulation leads to a \textit{min-max} problem. We provide a numerical scheme for solving this problem when a finite number of vanilla option prices are available. Numerical results on the hedging performance of this model-free approach when the option prices are generated using a \textit{Black-Scholes} and a \textit{Merton Jump diffusion} model are presented. We also provide theoretical bounds on the hedging error at $T$, the maturity of the target option.

q-fin.MF↗

arXiv2023

Multi-period static hedging of European options

We consider the hedging of European options when the price of the underlying asset follows a single-factor Markovian framework. By working in such a setting, Carr and Wu \cite{carr2014static} derived a spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this paper, we have extended their approach to simultaneously include options over multiple short maturities. We then show a practical implementation of this with a finite set of shorter-term options to determine the hedging error using a Gaussian Quadrature method. We perform a wide range of experiments for both the \textit{Black-Scholes} and \textit{Merton Jump Diffusion} models, illustrating the comparative performance of the two methods.

q-fin.MF↗

arXiv2017

Capacity of Cellular Wireless Network

Earlier definitions of capacity for wireless networks, e.g., transport or transmission capacity, for which exact theoretical results are known, are well suited for ad hoc networks but are not directly applicable for cellular wireless networks, where large-scale basestation (BS) coordination is not possible, and retransmissions/ARQ under the SINR model is a universal feature. In this paper, cellular wireless networks, where both BS locations and mobile user (MU) locations are distributed as independent Poisson point processes are considered, and each MU connects to its nearest BS. With ARQ, under the SINR model, the effective downlink rate of packet transmission is the reciprocal of the expected delay (number of retransmissions needed till success), which we use as our network capacity definition after scaling it with the BS density. Exact characterization of this natural capacity metric for cellular wireless networks is derived. The capacity is shown to first increase polynomially with the BS density in the low BS density regime and then scale inverse exponentially with the increasing BS density. Two distinct upper bounds are derived that are relevant for the low and the high BS density regimes. A single power control strategy is shown to achieve the upper bounds in both the regimes. This result is fundamentally different from the well known capacity results for ad hoc networks, such as transport and transmission capacity that scale as the square root of the (high) BS density. Our results show that the strong temporal correlations of SINRs with PPP distributed BS locations is limiting, and the realizable capacity in cellular wireless networks in high-BS density regime is much smaller than previously thought. A byproduct of our analysis shows that the capacity of the ALOHA strategy with retransmissions is zero.

cs.IT↗

arXiv2013

Percolation on the Information-Theoretically Secure Signal to Interference Ratio Graph

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes (PPPs) in $\bbR ^2$ of intensities $λ$ and $λ_E$ respectively. A directed edge from one legitimate node $A$ to another legitimate node $B$ exists provided the strength of the {\it signal} transmitted from node $A$ that is received at node $B$ is higher than that received at any eavesdropper node. The strength of the received signal at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter $γ$. The graph is said to percolate when there exists an infinite connected component. We show that for any finite intensity $λ_E$ of eavesdropper nodes, there exists a critical intensity $λ_c < \infty$ such that for all $λ> λ_c$ the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the sub-critical regime, we show that there exists a $λ_0$ such that for all $λ< λ_0 \leq λ_c$ a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

cs.IT↗

arXiv2007

Critical Age Dependent Branching Markov Processes and Their Scaling Limits

This paper studies: (i) the long time behaviour of the empirical distribution of age and normalised position of an age dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age dependent critical branching Brownian motions.

math.PR↗