Agent-based mapping of credit risk for sustainable microfinance

Inspired by recent ideas on how the analysis of complex financial risks can benefit from analogies with independent research areas, we propose an unorthodox framework for mapping microfinance credit risk---a major obstacle to the sustainability of lenders outreaching to the poor. Specifically, using the elements of network theory, we constructed an agent-based model that obeys the stylised rules of microfinance industry. We found that in a deteriorating economic environment confounded with adverse selection, a form of latent moral hazard may cause a regime shift from a high to a low loan repayment probability. An after-the-fact recovery, when possible, required the economic environment to improve beyond that which led to the shift in the first place. These findings suggest a small set of measurable quantities for mapping microfinance credit risk and, consequently, for balancing the requirements to reasonably price loans and to operate on a fully self-financed basis. We illustrate how the proposed mapping works using a 10-year monthly data set from one of the best-known microfinance representatives, Grameen Bank in Bangladesh. Finally, we discuss an entirely new perspective for managing microfinance credit risk based on enticing spontaneous cooperation by building social capital.Comment: 9 pages, 5 figure

The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate

The Fastest Evolutionary Trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.MathematicsOrganismic and Evolutionary Biolog

A Symmetry of Fixation Times in Evoultionary Dynamics

In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright–Fisher models, nor when the mutants start from multiple copies.Human Evolutionary BiologyMathematic

Optimal growth model for the latitudinal cline of shell morphology in cowries (genus Cypraea

ABSTRACT The marine Indo-Pacific cowry, Cypraea caputserpentis, shows geographic variation of life history and shell morphology. Adult body size increases with latitude, but shell thickness decreases with latitude. To explain the clinal variations, we study a mathematical model of the optimal growth schedule. The life history of cowries consists of three stages: shell volume increases in the juvenile stage, which is followed by the callus-building stage in which shell thickness increases, and then reproduction starts without further growth in the adult stage. We calculate the lengths of juvenile and callus-building stages that maximize lifetime reproduction. By considering latitudinal change in the mortality and growth-promoting factors, the observed clinal patterns of juvenile traits can be explained by a negative latitudinal gradient of shell-crushing predators. This suggests the importance of a latitudinal gradient of predation pressure for body-size clines in marine ectotherms. On the other hand, latitudinal clines of shell thickness can be explained by a latitudinal gradient of either shell-crushing predation pressure or one of the environmental factors promoting shell thickening, such as seawater temperature

Stochastic Tunneling of Two Mutations in a Population of Cancer Cells

Cancer initiation, progression, and the emergence of drug resistance are driven by specific genetic and/or epigenetic alterations such as point mutations, structural alterations, DNA methylation and histone modification changes. These alterations may confer advantageous, deleterious or neutral effects to mutated cells. Previous studies showed that cells harboring two particular alterations may arise in a fixed-size population even in the absence of an intermediate state in which cells harboring only the first alteration take over the population; this phenomenon is called stochastic tunneling. Here, we investigated a stochastic Moran model in which two alterations emerge in a cell population of fixed size. We developed a novel approach to comprehensively describe the evolutionary dynamics of stochastic tunneling of two mutations. We considered the scenarios of large mutation rates and various fitness values and validated the accuracy of the mathematical predictions with exact stochastic computer simulations. Our theory is applicable to situations in which two alterations are accumulated in a fixed-size population of binary dividing cells

Human movement decisions during Coronavirus Disease 2019

To predict epidemics' future course in changing situations, understanding human mobility patterns is important, notwithstanding decision-making process uncertainties owing to difficulties in quantifying people's mobility change decision timings, which make the mobility-epidemic causal relationship unclear. We used the 'mobility avoidance index' to investigate time-series changes during Japan's Coronavirus Disease 2019 (eight waves until February 2023) as a previous study, which measured this index using accommodation reservation data-booking/cancellation timings-was able to quantify the timing of decision-making for mobility changes. Our analyses revealed two general patterns: 1) the index increased/decreased proportional to logarithms of reported cases during the first wave, conforming with Weber-Fechner's psychophysics law; 2) its slope against the change in the number of reported cases had similar values among the waves, but its intercepts changed as the waves passed, suggesting that people neglected reported cases lower than a certain threshold for behavioural decision-making. We shifted the threshold level as the waves passed, and named this pattern 'shift of negligible epidemic' rule. It is the first pattern quantitatively observed, that possesses decision making tendencies for future mobility avoidance. Our findings contribute to constructing a mathematical model, which simultaneously considers epidemics and human mobility dynamics