A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

In this work, we propose a new method for modeling human reasoning about objects’ similarities. We assume that similarity depends on perceived intensities of objects’ attributes expressed by natural language expressions such as low, medium, and high. We show how to find the underlying structure of the matrix with intensities of objects’ similarities in the factor-analysis-like manner. The demonstrated approach is based on fuzzy logic and set theory principles, and it uses only maximum and minimum operators. Similarly to classic eigenvector decomposition, we aim at representing the initial linguistic ordinal-scale (LOS) matrix as a max–min product of other LOS matrix and its transpose. We call this reconstructing matrix a neuromatrix because we assume that such a process takes place at the neural level in our brain. We show and discuss on simple, illustrative examples, how the presented way of modeling grasps natural way of reasoning about similarities. The unique characteristics of our approach are treating smaller attribute intensities as less important in making decisions about similarities. This feature is consistent with how the human brain is functioning at a biological level. A neuron fires and passes information further only if input signals are strong enough. The proposal of the heuristic algorithm for finding the decomposition in practice is also introduced and applied to exemplary data from classic psychological studies on perceived similarities between colors and between nations. Finally, we perform a series of simulation experiments showing the effectiveness of the proposed heuristic.

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“…[102][103][104][105][106][107][108]), their fuzzy equivalents (see [109][110][111]), or even Markov switching models (cf. [112,113]).…”

Section: Validation Studiesmentioning

confidence: 99%

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Grobelny

Michalski

Weber

2020

Neural Comput & Applic

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“…This paper is devoted to the foundations of semialgebraic gene-environment networks, i.e., to bases of the future development of algorithmic methods to assess those networks and to real-work applications. Already today we may mention that the following refined classes of techniques can be naturally suggested for our new class of networks under uncertainty, for their identification, optimization and extension: (i) Tchebychev Approximation [53], (ii) Semi-Infinite Optimization [29], (iii) Generalized Semi-Infinite Optimization [48,49,56], (iv) Bi-level and Multilevel Optimization [36], (v) Disjunctive Optimization [2], (vi) Robust Optimization [24,39,42], (vii) Conic Optimization [4], (viii) Optimal Control [1], and (ix) Stochastic Optimal Control [33]. Concerning classes of future real-world applications we would like to recommend emerging challenges of, for example, (a) Collaborative Games under Ellipsoidal Uncertainty or (per inner or outer approximations) Hypercube Uncertainty [11,52], (b) Transportation ("Piano Mover's" and many more) problems [32,40], (c) Supply Chain and Inventory Management [12,20,30,41,43,57] Production Planning [38], various kinds of (d) Design problems [46], (e) Artificial Intelligence and Machine Learning (e.g., "Infinite Kernel Learning") [6,13,28], and (f ) Finance, Actuarial Sciences and Pension Fund Systems [14,19,55].…”

Section: Definition 52 a Parameter-dependent Target-environment Netmentioning

confidence: 99%

Foundations of semialgebraic gene-environment networks

Kropat¹,

Weber²,

Tirkolaee³

2020

Journal of Dynamics &Amp; Games

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Gene-environment network studies rely on data originating from different disciplines such as chemistry, biology, psychology or social sciences. Sophisticated regulatory models are required for a deeper investigation of the unknown and hidden functional relationships between genetic and environmental factors. At the same time, various kinds of uncertainty can arise and interfere with the system's evolution. The aim of this study is to go beyond traditional stochastic approaches and to propose a novel framework of semialgebraic gene-environment networks. Foundation is laid for future research, methodology and application. This approach is a natural extension of interconnected systems based on stochastic, polyhedral, ellipsoidal or fuzzy (linguistic) uncertainty. It allows for a reconstruction of the underlying network from uncertain (semialgebraic) data sets and for a prediction of the uncertain futures states of the system. In addition, aspects of network pruning for large regulatory systems in genome-wide studies are discussed leading to mixed-integer programming (MIP) and continuous programming.

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“…The applications of robust optimization arises in many field such as finance [21][22][23], control [24] and supply chain management [25]. Ozmen et al [21] proposed the methodology that generated the future scenarios through Robust Conic Multivariate Adaptive Regression Splines (RCMARS) that mitigates data uncertainty.…”

Section: Stochastic Programming and Robust Optimizationmentioning

confidence: 99%

Performance evaluation for distributionally robust optimization with binary entries

Ohmori

Yoshimoto

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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We consider the data-driven stochastic programming problem with binary entries where the probability of existence of each entry is not known, instead realization of data is provided. We applied the distributionally robust optimization technique to minimize the worst-case expected cost taken over the ambiguity set based on the Kullback-Leibler divergence. We investigate the out-of-sample performance of the resulting optimal decision and analyze its dependence on the sparsity of the problem.

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A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

Cited by 125 publications

References 16 publications

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Foundations of semialgebraic gene-environment networks

Performance evaluation for distributionally robust optimization with binary entries

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