We study a financial market where the risky asset is modelled by a stochastic differential equation driven by a partially reflected Brownian motion. This models a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier in order to prevent it from going below that barrier. See e.g. Jarrow & Protter for an explanation and discussion of this model. This corresponds to a local time term in the equation for the asset price. As already pointed out by Karatzas & Shreve (see also Jarrow & Protter ) this allows for arbitrages in the market. In this paper we consider the case when there is a delay $\theta> 0$ in the information flow available for the trader. Using white noise and Hida-Malliavin calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as $\theta> 0$. This implies that there is no arbitrage in the market in that case. However, when $\theta$ goes to 0, the value goes to infinity. This is in agreement with the above result that is an arbitrage when there is no delay.

We study the optimal management of a collectivised pension fund, where all investors agree that the assets of deceased members are shared among the survivors. We find that for realistic parameters based on the UK pensions market, a collectivised fund achieves an approximately 20% better return than either an annuity or a personal investment fund.

We introduce models of investor preferences over a stream of pension payments in the presence of mortality, incorporating a new concept of adequacy. We find that for risk-averse individuals, pension adequacy plays an important role in determining the optimal fund management strategy.

A key issue in the design of collective funds is how to ensure the fund treats all investors fairly. This is a trivial problem in the case that all investors have identical preferences, wealth and mortality, but becomes challenging for heterogeneous funds. We give a strategy for the management of heterogeneous funds in complete markets and prove that it is asymptotically optimal in the absence of systematic longevity risk.

Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is in the sense that we can compare and contrast data streams regardless of where and how they are generated and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing, and vastly improves discrimination performance and computing speed. The core idea here is the generalization of the notion of KL divergence often used to compare probability distributions to a notion of divergence in time series. We call this the sequence likelihood (SL) divergence, which may be used to measure deviations within a well-defined class of discrete-valued stochastic processes. We devise efficient estimators of SL divergence from finite sample paths and subsequently formulate a universal metric useful for computing distance between time series produced by hidden stochastic generators.

Today's service companies operate in a technology-oriented and knowledge-intensive environment while recruiting and training individuals from an increasingly diverse population. One of the resulting challenges is ensuring strategic alignment between their two key resources - technology and workforce - through the resource planning and allocation processes. The traditional hierarchical decision approach to resource planning and allocation considers only technology planning as a strategic-level decision, with workforce recruiting and training planning as a subsequent tactical-level decision. However, two other decision approaches - joint and integrated - elevate workforce planning to the same strategic level as technology planning. Thus we investigate the impact of strategically aligning technology and workforce decisions through the comparison of joint and integrated models to each other and to a baseline hierarchical model in terms of the total cost. Numerical experiments are conducted to characterize key features of solutions provided by these approaches under conditions typically found in this type of service company. Our results show that the integrated model is the lowest cost across all conditions. This is because the integrated approach maintains a small but skilled workforce that can operate new and more advanced technology with higher capacity. However, the cost performance of the joint model is very close to the integrated model under many conditions and is easier to implement computationally and managerially, making it a good choice in many environments. Managerial insights derived from this study can serve as a valuable guide for choosing the proper decision approach for technology-oriented and knowledge-intensive service companies.

In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several rank-size distributions from different context in Arts and Sciences, as a two-parameter generalization of Zipf's law. Although it has been seen to provide excellent fits for several real world empirical datasets, the underlying theory responsible for the success of this particular rank order distribution is not explored properly. Here we, for the first time, provide its generating process which describes it as a natural maximum entropy distribution under an appropriate bivariate utility constraint. Further, considering the similarity of the proposed utility function with the usual logarithmic utility function from economic literature, we have also explored its acceptability in universal modeling of different types of socio-economic factors within a country as well as across the countries. The values of distributional parameters estimated through a rigorous statistical estimation method, along with the $entropy$ values, are used to characterize the distributions of all these socio-economic factors over the years.

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the monotonicity of the Gini index in the usual stochastic order proposed by Samanthi, Wei and Brazauskas (2016) and Kim and Kim (2019) are also suitable for multivariate elliptical risks. We also study the tail probability of Gini index for multivariate elliptical risks and revised a large deviation result for the Gini indexes of multivariate normal risks in Kim and Kim (2019).

In this paper, we investigate the impact of the social media data in predicting the Tehran Stock Exchange (TSE) variables for the first time. We consider the closing price and daily return of three different stocks for this investigation. We collected our social media data from Sahamyab.com/stocktwits for about three months. To extract information from online comments, we propose a hybrid sentiment analysis approach that combines lexicon-based and learning-based methods. Since lexicons that are available for the Persian language are not practical for sentiment analysis in the stock market domain, we built a particular sentiment lexicon for this domain. After designing and calculating daily sentiment indices using the sentiment of the comments, we examine their impact on the baseline models that only use historical market data and propose new predictor models using multi regression analysis. In addition to the sentiments, we also examine the comments volume and the users' reliabilities. We conclude that the predictability of various stocks in TSE is different depending on their attributes. Moreover, we indicate that for predicting the closing price only comments volume and for predicting the daily return both the volume and the sentiment of the comments could be useful. We demonstrate that Users' Trust coefficients have different behaviors toward the three stocks.