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Register a new userDynamic investment model of the life cycle of a company under the influence of factors in a competitive environment
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Modelling all possible life cycles of a company in a highly competitive economic environment gives a significant advantage to the owner in his business investment activities. This article proposes and analyses a dynamic model of a companys life cycle with known action costs and transition probabilities, that can be affected by an outside influence. For this task, the Markov model was utilized. The proposed model is illustrated on a task of determining an advertising policy for a car dealership, that would increase the stock equity of a company. The result demonstrates the usefulness of a model for use in determining future actions of a company. We also review multiple models of the influence of outside factors on a companys total capitalization.
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Micha{l} Chorowski
, Ryszard Kutner College of Inter Facultyn Individual Studies in Mathematics
, Natural Sciences University of Warsaw
2020
Modern technology and innovations are becoming more crucial than ever for the survival of companies in the market. Therefore, it is significant both from theoretical and practical points of view to understand how governments can influence technology growth and innovation diffusion (TGID) processes. We propose a simple but essential extension of Ausloos-Clippe-Pc{e}kalski and related Cichy numerical models of the TGID in the market. Both models are inspired by the nonlinear non-equilibrium statistical physics. Our extension involves a parameter describing the probability of government intervention in the TGID process in the company market. We show, using Monte Carlo simulations, the effects interventionism can have on the companies market, depending on the segment of firms that are supported. The high intervention probability can result, paradoxically, in the destabilization of the market development. It lowers the markets technology level in the long-time limit compared to markets with a lower intervention parameter. We found that the intervention in the technologically weak and strong segments of the company market does not substantially influence the market dynamics, compared to the intervention helping the middle-level companies. However, this is still a simple model which can be extended further and made more realistic by including other factors. Namely, the cost and risk of innovation or limited government resources and capabilities to support companies.
In this article we solve the problem of maximizing the expected utility of future consumption and terminal wealth to determine the optimal pension or life-cycle fund strategy for a cohort of pension fund investors. The setup is strongly related to a DC pension plan where additionally (individual) consumption is taken into account. The consumption rate is subject to a time-varying minimum level and terminal wealth is subject to a terminal floor. Moreover, the preference between consumption and terminal wealth as well as the intertemporal coefficient of risk aversion are time-varying and therefore depend on the age of the considered pension cohort. The optimal consumption and investment policies are calculated in the case of a Black-Scholes financial market framework and hyperbolic absolute risk aversion (HARA) utility functions. We generalize Ye (2008) (2008 American Control Conference, 356-362) by adding an age-dependent coefficient of risk aversion and extend Steffensen (2011) (Journal of Economic Dynamics and Control, 35(5), 659-667), Hentschel (2016) (Doctoral dissertation, Ulm University) and Aase (2017) (Stochastics, 89(1), 115-141) by considering consumption in combination with terminal wealth and allowing for consumption and terminal wealth floors via an application of HARA utility functions. A case study on fitting several models to realistic, time-dependent life-cycle consumption and relative investment profiles shows that only our extended model with time-varying preference parameters provides sufficient flexibility for an adequate fit. This is of particular interest to life-cycle products for (private) pension investments or pension insurance in general.
In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the problem that one entity tries to block the influence propagation of its competing entity as much as possible by strategically selecting a number of seed nodes that could initiate its own influence propagation. We call this problem the influence blocking maximization (IBM) problem. We prove that the objective function of IBM in the CLT model is submodular, and thus a greedy algorithm could achieve 1-1/e approximation ratio. However, the greedy algorithm requires Monte-Carlo simulations of competitive influence propagation, which makes the algorithm not efficient. We design an efficient algorithm CLDAG, which utilizes the properties of the CLT model, to address this issue. We conduct extensive simulations of CLDAG, the greedy algorithm, and other baseline algorithms on real-world and synthetic datasets. Our results show that CLDAG is able to provide best accuracy in par with the greedy algorithm and often better than other algorithms, while it is two orders of magnitude faster than the greedy algorithm.
The interpretation of sampling data plays a crucial role in policy response to the spread of a disease during an epidemic, such as the COVID-19 epidemic of 2020. However, this is a non-trivial endeavor due to the complexity of real world conditions and limits to the availability of diagnostic tests, which necessitate a bias in testing favoring symptomatic individuals. A thorough understanding of sampling confidence and bias is necessary in order make accurate conclusions. In this manuscript, we provide a stochastic model of sampling for assessing confidence in disease metrics such as trend detection, peak detection, and disease spread estimation. Our model simulates testing for a disease in an epidemic with known dynamics, allowing us to use Monte-Carlo sampling to assess metric confidence. This model can provide realistic simulated data which can be used in the design and calibration of data analysis and prediction methods. As an example, we use this method to show that trends in the disease may be identified using under $10000$ biased samples each day, and an estimate of disease spread can be made with additional $1000-2000$ unbiased samples each day. We also demonstrate that the model can be used to assess more advanced metrics by finding the precision and recall of a strategy for finding peaks in the dynamics.
We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy.
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