Bi-directional grid absorption barrier constrained stochastic processes with applications in finance and investment

Whilst the gambler’s ruin problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required for the grid trading problem (GTP) of financial markets, especially foreign exchange (FX) markets. As banks and financial institutions have the requirement to hedge their FX exposure, the GTP can help provide a framework for greater automation of the hedging process and help forecast which hedge scenarios to avoid. Two theorems are adapted from GRP to GTP and prove that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. We introduce two absorption barriers, one at zero balance (ruin) and one at a specified profit target. This extends the traditional GRP and the GTP further by deriving both the probability of ruin and the expected number of steps (of reaching a barrier) to better demonstrate that GTP takes longer to reach ruin than GRP. These statistical results have applications into finance such as multivariate dynamic hedging (Noorian, Flower, & Leong, 2016), portfolio risk optimization, and algorithmic loss recovery

Buffer-gas cooling of molecules in the low-density regime: comparison between simulation and experiment

Cryogenic buffer gas cells have been a workhorse for the cooling of molecules in the last decades. The straightforward sympathetic cooling principle makes them applicable to a huge variety of different species. Notwithstanding this success, detailed simulations of buffer gas cells are rare, and have never been compared to experimental data in the regime of low to intermediate buffer gas densities. Here, we present a numerical approach based on a trajectory analysis, with molecules performing a random walk in the cell due to collisions with a homogeneous buffer gas. This method can reproduce experimental flux and velocity distributions of molecules emerging from the buffer gas cell for varying buffer gas densities. This includes the strong decrease in molecule output from the cell for increasing buffer gas density and the so-called boosting effect, when molecules are accelerated by buffer-gas atoms after leaving the cell. The simulations provide various insights which could substantially improve buffer-gas cell design

The model of the finite time ruin probabilities for insurance company with investment activities

Данная статья посвящена исследованию и разработке актуарной модели расчета времени наступления банкротства для страховой компании. Новизна статьи заключается в том, что анализируется страховая компания, которая осуществляет инвестиционную активность, что в свою очередь выступает в качестве дополнительной статьи ее дохода

Homo Aleator: a sociological study of gambling in western society

The subject of this thesis is the nature and form of gambling in western society. Unlike other academic studies, which approach the subject in piecemeal fashion and treat it as essentially problematic, this research aims to provide a comprehensive analysis of the activity by situating the phenomenological experience of modern gambling within a formal and historical framework, and examining it from a variety of theoretical perspectives. This thesis is divided into five Chapters. The first describes the historical development of the concept of chance and argues that, after a lengthy period in which it existed first as a sacred and later as an epistemological category, in the twentieth century chance was secularised and ascribed ontological status as an explanatory feature of the modern world. In Chapter Two, a study of the historical development of gambling forms, the social affiliation of the various groups associated with them complements the outline of chance given in Chapter One. Here it is argued that the nature of these games reflected wider social attitudes towards the perception of randomness, and also the general configuration of the society in which they were played. The development of games from their genesis in divination ritual to their formation into a recognisably modern gambling economy, is also traced, and the historical specificity of their various forms examined. The formal parameters and phenomenological experience of the gambling economy - the 'phenomenological sites' - is the subject of Chapter Three. It is argued that commercial organisation of games of chance in the late twentieth century is beginning to overcome the traditional stratification that for years has determined the social formation of gambling forms

Markov decision processes on finite spaces with fuzzy total rewards

summary:The paper concerns Markov decision processes (MDPs) with both the state and the decision spaces being finite and with the total reward as the objective function. For such a kind of MDPs, the authors assume that the reward function is of a fuzzy type. Specifically, this fuzzy reward function is of a suitable trapezoidal shape which is a function of a standard non-fuzzy reward. The fuzzy control problem consists of determining a control policy that maximizes the fuzzy expected total reward, where the maximization is made with respect to the partial order on the $\alpha$-cuts of fuzzy numbers. The optimal policy and the optimal value function for the fuzzy optimal control problem are characterized by means of the dynamic programming equation of the standard optimal control problem and, as main conclusions, it is obtained that the optimal policy of the standard problem and the fuzzy one coincide and the fuzzy optimal value function is of a convenient trapezoidal form. As illustrations, fuzzy extensions of an optimal stopping problem and of a red-black gambling model are presented

RISK AND UNCERTAINTY (UTILITY, DECISION)

The conventional theory of decision making under risk relies on axioms that reflect assumptions about people\u27s subjective attitudes towards wealth. The assumptions are unverifiable, and the axioms are too restrictive. They forbid some decision rules that a plausibly rational decision maker ( DM ) could find useful. A new method, at once less restrictive and less dependent upon subjective assumptions, motivates expected utility techniques by assuming that a DM wishes to place an upper limit on the probability of ruin. All bounded-above, increasing functions defined over a suitable domain can serve as utility functions. Now, DM can evaluate lotteries according to their buying prices, useful if one plans to withdraw capital from risk. DM can rigorously distinguish once in a lifetime lotteries from ordinary gambles; that\u27s helpful when facing Allais\u27 problem. Also, DM can exploit partial knowledge of state probabilities without choosing arbitrary point estimates for all uncertain odds. That helps to resolve problems that combine elements of both risk and uncertainty, like Ellsberg\u27s. The new method allows DM to do everything permitted under the old axioms, and more besides, with fewer and less ambitious assumptions

An analysis of industrial company failure in the UK and Russia for the 1990s

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis provides an examination of the key determinants of industrial company failure in the UK and Russia, for the 1990s. For the UK, some new empirical evidence, presented for the 1990s recession period, is based on binary logit analyses of a cross-section and unbalanced panel of large quoted companies, using accounting-based indicators. Conventional for cross sectional studies empirical design of modelling the failure determinants separately for various risk-horizons, prior to the event of insolvency, is extended here by allowing for unanticipated changes in the nominal interest rate and in the real exchange rate, and also by controlling for the firm's age effect. We find that cross sectional models, conditioned on changes in overall economic conditions, dominate simpler models, utilising financial inputs alone, for comparisons of ex ante, out-of sample classificatory accuracy. Thus, the UK data suggest that for the years before and during the 1990s recession, shifts in the real exchange rate and rises in the nominal interest rate magnified dramatically the risk of failure of highly geared firms. The estimates from the fixed effects models indicate substantial unobserved heterogeneity across members of the panel and reveal that failing UK companies were less liquid, lacked profitability, and had declining net worth. For Russia, the evidence from binary logit is bootstrap-based and controlled by comparison with a similar random sample drawn for the UK over the recession years 1990-91. The Russian data uncover that, unlike in the UK, gearing and liquidity did not appear to explain enterprise liquidation in the mid-1990s, while lower profitability and smaller size were the key determinants of failure risk.Financial support from the ACE Tacis Programme, Contract T95-5127-S in 1996-98, and from the Department of Economics and Finance of Brunel University in 1999-2000 were used in this work