Between the Gift and the Market: The Economy of Regard..

'The great transformation' from customary exchange to impersonal markets is incomplete. Reciprocal exchange pervades modern societies. it takes the form of 'gifts,' reciprocated without certainty. Reciprocity is driven by the pursuit of 'regard'. Money is avoided in regard exchanges, because it is impersonal. Instead, regard signals are embodied in goods, in services, or in time (attention). The personalization of gifts authenticates the signal. Reciprocal exchange persists in family formation, in intergenerational transfers, in labor markets, in agriculture, the professions, in marketing, entrepreneurship, and also in corruption and crime. Reciprocal exchange is constrained by the time and psychic energy, but is likely to persist as a preferred source of regard.

Two-sided reflected Markov-modulated Brownian motion with applications to fluid queues and dividend payouts

In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary distribution of this Markov process, which in addition to the complication of having a stochastic boundary can also include jumps at state change epochs of the underlying Markov chain because of the boundary changes. We give the general theory and then specialize to the case where the underlying Markov chain has two states. Moreover, motivated by an application of optimal dividend strategies, we consider the case where the lower barrier is zero and the upper barrier is subject to control. In this case we generalized earlier results from the case of a reflected Brownian motion to the Markov modulated case.Comment: 22 pages, 1 figur

A new formula for some linear stochastic equations with applications

We give a representation of the solution for a stochastic linear equation of the form $X_t=Y_t+\int_{(0,t]}X_{s-} \mathrm {d}{Z}_s$ where $Z$ is a c\'adl\'ag semimartingale and $Y$ is a c\'adl\'ag adapted process with bounded variation on finite intervals. As an application we study the case where $Y$ and $-Z$ are nondecreasing, jointly have stationary increments and the jumps of $-Z$ are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) processes and clearing processes. When $Y$ and $Z$ are, in addition, independent L\'evy processes, the resulting $X$ is called a generalized Ornstein-Uhlenbeck process.Comment: Published in at http://dx.doi.org/10.1214/09-AAP637 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Useful martingales for stochastic storage processes with L\'{e}vy-type input

In this paper we generalize the martingale of Kella and Whitt to the setting of L\'{e}vy-type processes and show that the (local) martingales obtained are in fact square integrable martingales which upon dividing by the time index converge to zero a.s. and in $L^2$. The reflected L\'{e}vy-type process is considered as an example.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1112.475

Modelling of Supercapacitors: Factors Influencing Performance

The utilizable capacitance of Electrochemical Double Layer Capacitors (EDLCs) is a function of the frequency at which they are operated and this is strongly dependent on the construction and physical parameters of the device. We simulate the dynamic behavior of an EDLC using a spatially resolved model based on the porous electrode theory. The model of Verbrugge and Liu (J. Electrochem. Soc. 152, D79 (2005)) was extended with a dimension describing the transport into the carbon particle pores. Our results show a large influence of the electrode thickness (Le), separator thickness (Ls) and electrolyte conductivity (κ) on the performance of EDLCs. In agreement with experimental data, the time constant was an increasing function of Le and Ls and a decreasing function of κ. The main limitation was found to be on the scale of the whole cell, while transport into the particles became a limiting factor only if the particle size was unrealistically large. The results were generalized into a simplified relation allowing for a quick evaluation of performance for the design of new devices. This work provides an insight into the performance limitation of EDLCs and identifies the critical parameters to consider for both systems engineers and material scientists