Search arXiv⌕ Search

arXiv · 0708.3467

Analytical modelling of terminal properties in industrial growth

Abstract

In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been addressed from a dynamical systems perspective, with especial emphasis on the concept of the Balanced Scorecard. Our study enables us to make the general claim that although the fortunes of an industrial organization can rise with exponential rapidity on relatively short time scales, its growth will ultimately and inevitably be saturated on long time scales by various factors which are nonlinear in character. We have mathematically demonstrated the likely occurrence of this feature under various possible circumstances, including the Red Ocean and the Blue Ocean. Finally and most importantly, our arguments and their associated mathematical modelling have received remarkable support from the growth pattern indicated by empirical data gathered from a well-recognized global company like IBM.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arnabi Marjit, Sudipto Marjit, Arnab K. Ray. 2008-04-25. Analytical modelling of terminal properties in industrial growth. https://arxiv.org/abs/0708.3467

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Exchange Rate Determination for Cryptocurrency Mergers: A Formal Framework

Many of the thousands of existing cryptocurrencies suffer from declining adoption, low liquidity and weak security, and merging two of them into a single ecosystem is a natural alternative to abandonment. No rigorous framework exists, however, for determining a fair exchange rate in such a merger. Unlike that of a corporation, the value of a cryptocurrency is driven by network effects, so the exchange rate itself influences the value of the merged asset. We extend the exchange-ratio framework of Mainini, Moretto and Visetti [7] by making the merged value endogenous: the exchange rate determines community migration, migration determines (up to user overlap) the post-merger network state, and an axiomatised valuation function assigns a value to that state. The resulting synergy has no predetermined sign, and the bounds of the bargaining region become self-referential in the exchange rate. We prove that no exchange rate at which the merger destroys value preserves wealth, and that the pre-merger price ratio preserves wealth exactly when the merger does not destroy value at that rate. In that case, under explicit threshold conditions, the price ratio satisfies all five of our fairness conditions -- wealth, adoption, security, governance and liquidity preservation -- and, under strict versions of these conditions, the admissible set contains a nondegenerate interval around it, the wealth-admissible set one of explicit width. The network-value laws proposed in the literature, from the linear law to Metcalfe's and its generalised power-law forms, share a convexity property that yields the Lipschitz control behind these estimates. Liquidity emerges as the only non-wealth condition that can disconnect the admissible set.

q-fin.GN↗

Firm Valuation When AI Shapes the Business Model: A Milestone-Based Real-Options Framework for the AI Valuation Uncertainty Problem

Standard valuation methods, including discounted cash flow, the income approach standard IDW S 1 of the Institute of Public Auditors in Germany, and market multiples, compress milestone probabilities, continuation options, and risk shifts into opaque aggregate parameters; none provides a structured protocol for decomposing AI integration into auditable option-level assumptions. We propose an industry-agnostic taxonomy separating AI Integrators from AI Providers. AI Integrators are further classified by their Integration Depth Level, ranging from no integration to AI at the core of the product or process. A milestone-gated real-options overlay decomposes milestone state value into five components, and an Analytic Hierarchy Process-based Success Readiness Index derives per-option probabilities from structured pairwise comparisons for scenario analysis. Applied to an AI-native energy software-as-a-service firm, the framework yields a coherent valuation band traceable to identifiable option-level assumptions. Risk concentrates in later-stage continuation options, matching the structural prediction for AI Providers. The protocol applies across the firm lifecycle, including mergers and acquisitions due diligence. The case is a single-firm demonstration of protocol coherence, not empirical validation; multi-case testing against realised post-exit valuations is left to future research.

q-fin.GN↗

Compliant AI Infrastructure for Regulated Finance: A tiered multi-agent framework with DLT audit trails for financial operations in DACH

We present a compliance-first architecture for AI in regulated finance that treats regulation as an orientation layer rather than a deterministic ruleset. A matrix of regulatory intent and exposure provides a compact classification handle, which a governed policy compiler then maps into concrete prohibitions, obligations and runtime budgets. Prohibitions constrain feasibility and block externalisation, while obligations extend tasks with artefacts that must meet explicit admissibility criteria. Committee activation remains policy-driven and proportionate, preserving efficiency while ensuring supervisory oversight. Evidence, decisions and reason codes are bound to a permissioned DAG with deterministic timestamping, enabling replay, provenance checks and clear attribution of failure. Clause-level legal indexing with effective dates and capability-based agent routing ensure portability across DACH and the wider EU. The result is assurance by construction: compliance is embedded in execution and verifiable by auditors without sacrificing proportionality or transparency.

q-fin.GN↗