Realistic Models of Financial Market and Structural Stability

The main aim of this article is to show the role of structural stability in financial modelling; that is, a specific “no-arbitrage” property is unaffected by small perturbations of the model’s dynamics. We prove that under the structural stability assumption, given a convex compact-valued multifunction, there exists a stochastic transition kernel with supports coinciding with this multifunction and one that is strong Feller in the strict sense. We also demonstrate preservation of structural stability for sufficiently small deviations of transition kernels for different probability metrics.

LifeSim: A Lifecourse Dynamic Microsimulation Model of the Millennium Birth Cohort in England

We present a novel dynamic microsimulation model that undertakes stochastic transition modelling of a rich set of developmental, economic, social and health outcomes from birth to death for each child in the Millennium Birth Cohort (MCS) in England. The model is implemented in R and draws initial conditions from the MCS by re-sampling a population of 100,000 children born in the year 2000, and simulates long-term outcomes using life-stage specific stochastic equations. Our equations are parameterised using effect estimates from existing studies combined with target outcome levels from up-to-date administrative and survey data. We present our baseline projections and a simple validation check against external data from the British Cohort Study 1970 and Understanding Society survey.

Modeling the transition of death assemblages from surface to subsurface: predicting the effects of burial, mixing, and disintegration on time averaging

<p>Although the temporal resolution and incompleteness of the fossil record are strongly determined by the thickness of the taphonomic active zone and by the depth and rate of mixing, it is unclear whether changes in time-averaging associated with the burial of assemblages that form in the surface mixed layer (SML) can be generalized across environments. Here we extend our previous models, which estimated disintegration on the basis of shell-age distributions (AFDs) in the SML, to stochastic transition matrices, and then apply them to discrete stratigraphic layers in sediment cores. This permits us to: (1) predict downcore trends in the shape of shell AFDs, and (2) estimate burial, disintegration, and mixing rates on the basis of age distributions observed in sediment cores. We find that, first, if the time to burial of individual shells to a specific sediment depth is stochastic due to bioturbation, then the inter-quartile age range will increase and skewness and kurtosis will decrease downcore to the top of permanent, historical layers (because the deepest layers reached by bioturbators are affected by mixing for a longer time than are surface layers). Systematic dm- to meter-scale changes in AFDs downcore can thus arise without changes in rates of sedimentation or mixing. Second, in contrast to expectations that species with durable shells will exhibit greater time averaging (larger inter-quartile age ranges) than species with fragile shells (an effect typical of assemblages in the SML), this difference will be minimized below the taphonomically active zone. Third, the median and modes of the AFDs of species differing in durability will differ, however, in those subsurface assemblages, producing age offsets (geologic age discordance) among species. These three predictions are clearly relevant for Holocene-Anthropocene studies, but also inform our understanding of deeper time fossil records, where episodically rapid burial can move surface assemblage to historical layers. In such case, the downcore decline in time averaging associated predicted by the surface-subsurface transition will characterize some subsets of stratigraphic successions in the fossil record.</p>

Critical slowing down associated with critical transition and risk of collapse in crypto-currency

The year 2017 saw the rise and fall of the crypto-currency market, followed by high variability in the price of all crypto-currencies. In this work, we study the abrupt transition in crypto-currency residuals, which is associated with the critical transition (the phenomenon of critical slowing down) or the stochastic transition phenomena. We find that, regardless of the specific crypto-currency or rolling window size, the autocorrelation always fluctuates around a high value, while the standard deviation increases monotonically. Therefore, while the autocorrelation does not display the signals of critical slowing down, the standard deviation can be used to anticipate critical or stochastic transitions. In particular, we have detected two sudden jumps in the standard deviation, in the second quarter of 2017 and at the beginning of 2018, which could have served as the early warning signals of two major price collapses that have happened in the following periods. We finally propose a mean-field phenomenological model for the price of crypto-currency to show how the use of the standard deviation of the residuals is a better leading indicator of the collapse in price than the time-series' autocorrelation. Our findings represent a first step towards a better diagnostic of the risk of critical transition in the price and/or volume of crypto-currencies.