arXiv subjects

Enrique A. Thomann

Publications and source records attributed to Enrique A. Thomann.

6 recordsLinked to original sources

arXiv2026

On the Impact of Insurance on Households Susceptible to Random Proportional Losses: An Analysis of Poverty Trapping

The trapping probability is studied for households' capital assuming that losses are proportional to the accumulated capital. We consider households without insurance and those purchasing proportional insurance. Parameter conditions under which poverty trapping is not certain in both cases are derived. For the uninsured model, a new closed-form expression for the trapping probability is obtained when the remaining proportion of capital after a loss has a beta distribution, showing that the trapping probability decays algebraically as the initial capital increases. When insurance is purchased and the remaining proportion is uniformly distributed, the trapping probability is computed by solving a non-local integro-differential equation. Our results show that insurance can prevent otherwise certain trapping in some cases, although it may increase trapping risk for households with initial capital barely above the poverty line, while reducing trapping risk for households with higher initial capital.

q-fin.RM↗

arXiv2026

Optimal Risk-Sharing Rules in Network-based Decentralized Insurance

This paper studies decentralized risk-sharing on networks. In particular, we consider a model where agents are nodes in a given network structure. Agents directly connected by edges in the network are referred to as friends. We study actuarially fair risk-sharing under the assumption that only friends can share risk, and we characterize the optimal signed linear risk-sharing rule in this network setting. Subsequently, we consider a special case of this model where all the friends of an agent take on an equal share of the agent's risk, and establish a connection to the graph Laplacian. Our results are illustrated with several examples.

math.OC↗

arXiv2023

Errata to Stochastic explosion and non-uniqueness for $α$-Riccati equation

An error occurs in a part of the statement and proof of Proposition 2.2 in Jour. Math. Anal. and Appl., 476, (2019), 53-85 that is corrected in this erratum. The revised result reveals a new and unexpected critical phenomenon, having further implications for non-uniqueness of solutions to a nonlinear differential equation of the Riccati type.

math.PR↗

arXiv2015

Continuity of Local Time: An applied perspective

Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension of previous results on an explicit role of continuity of (natural) local time is obtained for applications to recent classes of problems in physics, biology and finance involving discontinuities in a dispersion coefficient. The main theorem and its corollary provide physical principles that relate macro scale continuity of deterministic quantities to micro scale continuity of the (stochastic) local time.

math.PR↗

arXiv2013

Advection-Dispersion Across Interfaces

This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with formulations in terms of partial differential equations governing the conservative, advective-dispersive transport of mass concentrations in divergence form, the specific interfacial heterogeneities are introduced in terms of (spatial) discontinuities in the diffusion coefficient across a lower-dimensional hypersurface. A pathway to an equivalent stochastic formulation is then developed with special attention to the interfacial effects in various functionals such as first passage times, occupation times and local times. That an appreciable theory is achievable within a framework of applications involving one-dimensional models having piecewise constant coefficients greatly facilitates our goal of a gentle introduction to some rather dramatic mathematical consequences of interfacial effects that can be used to predict structure and to inform modeling.

math.ST↗

arXiv2011

First Passage Times and Breakthrough Curves Associated with Interfacial Phenomena

Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A mathematical framework is formulated to address specific empirical phenomena involving first passage time and occupation time functionals observed in relation to the interfacial parameters.

math.PR↗