We embrace a fresh perspective to auditing by analyzing a large set of companies as complex financial networks rather than static aggregates of balance sheet data. Preliminary analyses show that network centrality measures within these networks could significantly enhance auditors' insights into financial structures. Utilizing data from over 300 diverse companies, we examine the structure of financial statement networks through bipartite graph analysis, exploring their scale-freeness by comparing degree distributions to power-law and exponential models. Our findings indicate heavy-tailed degree distribution for financial account nodes, networks that grow with the same diameter, and the presence of influential hubs. This study lays the groundwork for future auditing methodologies where baseline network statistics could serve as indicators for anomaly detection, marking a substantial advancement in audit research and network science.

Auditing is a multi-billion dollar market, with auditors assessing the trustworthiness of financial data, contributing to financial stability in a more interconnected and faster-changing world. We measure cross-sectoral structural similarities between firms using microscopic real-world transaction data. We derive network representations of companies from their transaction datasets, and we compute an embedding vector for each network. Our approach is based on the analysis of 300+ real transaction datasets that provide auditors with relevant insights. We detect significant changes in bookkeeping structure and the similarity between clients. For various tasks, we obtain good classification accuracy. Moreover, closely related companies are near in the embedding space while different industries are further apart suggesting that the measure captures relevant aspects. Besides the direct applications in computational audit, we expect this approach to be of use at multiple scales, from firms to countries, potentially elucidating structural risks at a broader scale.

We develop a novel framework using Bayesian networks to capture distress dependence in the context of counterparty credit risk. This allows us to calibrate the probability of distress of an entity conditional on the distress of a different entity. We apply our methodology to wrong-way risk model proposed by Turlakov and stress scenario testing. Our results show that stress propagation in an interconnected financial system can have a significant impact on counterparty credit exposures.

The robustness of credit portfolio models is of great interest for financial institutions and regulators, since misspecified models translate into insufficient capital buffers and a crisis-prone financial system. In this paper, the authors propose a method to enhance credit portfolio models based on the model of Merton by incorporating contagion effects. While, in most models, the risks related to financial interconnectedness are neglected, the authors use Bayesian network methods to uncover the direct and indirect relationships between credits while maintaining the convenient representation of factor models. A range of techniques to learn the structure and parameters of financial networks from real credit default swaps data are studied and evaluated. Their approach is demonstrated in detail in a stylized portfolio, and the impact on standard risk metrics is estimated.

Accounting scandals like Enron (2001) and Petrobas (2014) remind us that untrustworthy financial information has an adverse effect on the stability of the economy and can ultimately be a source of systemic risk. This financial information is derived from processes and their related monetary flows within a business. But as the flows are becoming larger and more complex, it becomes increasingly difficult to distill the primary processes for large amounts of transaction data. However, by extracting the primary processes we will be able to detect possible inconsistencies in the information efficiently. We use recent advances in network embedding techniques that have demonstrated promising results regarding node classification problems in domains like biology and sociology. We learned a useful continuous vector representation of the nodes in the network which can be used for the clustering task, such that the clusters represent the meaningful primary processes. The results show that we can extract the relevant primary processes which are similar to the created clusters by a financial expert. Moreover, we construct better predictive models using the flows from the extracted primary processes which can be used to detect inconsistencies. Our work will pave the way towards a more modern technology and data-driven financial audit discipline.

Auditors use predictive models to estimate financial account values in a financial statement. Prior studies suggest that incorporating organizational knowledge into these models yields better predictive accuracy. We propose a novel method to construct a financial statement network in order to gain insight into the organizational structure of a company using real financial transaction data from ten companies. We show that real data yields financial statement networks of varying complexity. We introduce a method to aggregate the nodes and edges of the financial statement network, which results in its visualization at the right level of tractability. We also show that this visualization enables the auditor to assess the complexity of the organizational structure of a company and to use it as a risk indicator for the audit. Further, the obtained network yields insights into the monetary flow between financial accounts and business processes. We show that this information can be used to add organizational knowledge to predictive models for the purpose of obtaining audit evidence.

Portfolio credit risk models estimate the range of potential losses due to defaults or deteriorations in credit quality. Most of these models perceive default correlation as fully captured by the dependence on a set of common underlying risk factors. In light of empirical evidence, the ability of such a conditional independence framework to accommodate for the occasional default clustering has been questioned repeatedly. Thus, financial institutions have relied on stressed correlations or alternative copulas with more extreme tail dependence. In this paper, we propose a different remedy—augmenting systematic risk factors with a contagious default mechanism which affects the entire universe of credits. We construct credit stress propagation networks and calibrate contagion parameters for infectious defaults. The resulting framework is implemented on synthetic test portfolios wherein the contagion effect is shown to have a significant impact on the tails of the loss distributions.

We introduce and study bisimulations for coalgebras on Stone spaces (Kupke et al., 2004, Theoretical Computer Science, 327, 109-134), motivated by previous work on ultrafilter extensions for coalge ...

The models used to calculate post-crisis valuation adjustments, market risk and capital measures for derivatives are subject to liquidity risk due to severe lack of available information to obtain market implied model parameters. The European Banking Authority has proposed an intersection methodology to calculate a proxy CDS or Bond spread. Due to practical issues of this method, Chourdakis et al. introduce a cross-section approach. In this paper, we extend the cross-section methodology using equity returns, and show that our methodology is significantly more accurate compared to both existing methodologies, and produces more reliable, stable and robust market risk and capital measures, and credit valuation adjustment.

We introduce a new order-topological semantics for the positive modal mu-calculus over modal compact Hausdorff spaces, which are generalizations of descriptive frames. We define Sahlqvist sequents in this language, prove Esakia's lemma and Sahlqvist preservation theorem for this semantics. We show that every Sahlqvist sequent has a frame correspondent in first-order logic with fixed-point operators.

By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras (complete Boolean algebras endowed with a proximity-like relation). We provide an alternative "modal-like" duality by introducing the concept of a Gleason space, which is a pair (X,R), where X is an extremally disconnected compact Hausdorff space and R is an irreducible equivalence relation on X. Our main result states that the category of Gleason spaces is equivalent to the category of compact Hausdorff spaces, and is dually equivalent to the category of de Vries algebras.

The present paper proposes a new introductory treatment of the very well known Sahlqvist correspondence theory for classical modal logic. The first motivation for the present treatment is a consideration regarding exposition: classical Sahlqvist correspondence is presented in a uniform and modular way, and, unlike the existing textbook accounts, extends itself to a class of formulas laying outside the Sahlqvist class proper. The second motivation is methodological: the present treatment aims at highlighting the algebraic and order-theoretic nature of the correspondence mechanism. The exposition remains elementary and does not presuppose any previous knowledge or familiarity with the algebraic approach to logic. However, it provides the underlying motivation and basic intuitions for the recent developments in the Sahlqvist theory of nonclassical logics, which compose the so-called unified correspondence theory.

We extend unified correspondence theory to Kripke frames with impossible worlds and their associated regular modal logics. These are logics the modal connectives of which are not required to be normal: only the weaker properties of additivityx.y=(x. y) and multiplicativityx.y=(x. y) are required. Conceptually, it has been argued that their lacking necessitation makes regular modal logics better suited than normal modal logics at the formalization of epistemic and deontic settings. From a technical viewpoint, regularity proves to be very natural and adequate for the treatment of algebraic canonicity Jonsson- style. Indeed, additivity and multiplicativity turn out to be key to extend Jonsson's original proof of canonicity to the full Sahlqvist class of certain regular distributive modal logics naturally generalizing distributive modal logic. Most interestingly, additivity and multiplicativity are key to Jonsson- style canonicity also in the original (i. e. normal) DML. Our contributions include: the definition of Sahlqvist inequalities for regular modal logics on a distributive lattice propositional base; the proof of their canonicity following Jonsson's strategy; the adaptation of the algorithm ALBA to the setting of regular modal logics on two non- classical (distributive lattice and intuitionistic) bases; the proof that the adapted ALBA is guaranteed to succeed on a syntactically defined class which properly includes the Sahlqvist one; finally, the application of the previous results so as to obtain proofs, alternative to Kripke's, of the strong completeness of Lemmon's epistemic logics E2- E5 with respect to elementary classes of Kripke frames with impossible worlds.

The theory of canonical extensions typically considers extensions of maps A→B to maps Aδ→Bδ. In the present article, the theory of canonical extensions of maps A→Bδ to maps Aδ→Bδ is developed, and is applied to obtain a new canonicity proof for those inequalities in the language of Distributive Modal Logic (DML) on which the algorithm ALBA [9] is successful.

In the present paper, the algorithmic correspondence theory developed in Conradie and Palmigiano [9] is extended to mu-calculi with a non-classical base. We focus in particular on the language of bi-intuitionistic modal mu-calculus. We enhance the algorithm ALBA introduced in Conradie and Palmigiano [9] so as to guarantee its success on the class of recursive mu-inequalities, which we introduce in this paper. Key to the soundness of this enhancement are the order-theoretic properties of the algebraic interpretation of the fixed point operators. We show that, when restricted to the Boolean setting, the recursive mu-inequalities coincide with the “Sahlqvist mu-formulas” defined in van Benthem, Bezhanishvili and Hodkinson [22].

We generalize Venema's result on the canonicity of the additivity of positive terms, from classical modal logic to a vast class of logics the algebraic semantics of which is given by varieties of normal distributive lattice expansions (normal DLEs), aka `distributive lattices with operators'. We provide two contrasting proofs for this result: the first is along the lines of Venema's pseudo-correspondence argument but using the insights and tools of unified correspondence theory, and in particular the algorithm ALBA; the second closer to the style of Jónsson. Using insights gleaned from the second proof, we define a suitable enhancement of the algorithm ALBA, which we use prove the canonicity of certain syntactically defined classes of DLE-inequalities (called the meta-inductive inequalities), relative to the structures in which the formulas asserting the additivity of some given terms are valid.

In this thesis we study correspondence and canonicity for non-classical logic using algebraic and order-topological methods. Correspondence theory is aimed at answering the question of how precisely modal, first-order, second-order languages interact and overlap in their shared semantic environment. The line of research in correspondence theory which concerns the present thesis is Sahlqvist correspondence theory --- which was originally developed for classical modal logic, and provides a systematic translation between classical modal logic and first-order logic. Canonicity is closely related to correspondence, and ensures that logics axiomatized by these formulas are complete with respect to relational semantics. Thus, correspondence and canonicity together establish that Sahlqvist logics are semantically complete with respect to first-order definable classes of relational structures. The first part of the thesis focuses on algebraic methods. In chapter 3, we prove the classical Sahlqvist correspondence theorem for basic modal logic in the algebraic setting of complex algebras of frames. We extend the algorithm ALBA to regular modal logic (modal logic with non-normal modalities) and intuitionistic modal mu-calculus in Chapters 4 and 5, respectively. In Chapter 6, we develop ALBA for distributive lattice expansions, using which we prove relativised canonicity for the meta-inductive inequalities. The second part of the thesis focuses on order-topological methods. In Chapter 7, we prove a modal-like duality for de Vries algebras. In Chapter 8, we prove a Sahlqvist correspondence and canonicity theorem for topological fixed-point logic on compact Hausdorff spaces.

We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [3]. The main result of our paper is that bisimulation for a Stone coalgebra is the topological closure of bisimulation for the underlying Set coalgebra.

Characterization of successful formulas in Public Announcement Logic (PAL) is a well known open problem in Dynamic Epistemic Logic. Recently, Holliday and ICard have given a complete characterization for the single agent case. However, the problem for the multi-agent case is open. This paper gives a partial solution to the problem, characterizing the subclass of the language consisting of unary operators, and discusses methods to give a complete solution.

Sahlqvist correspondence theory [3], [4] is one of the most important and useful results of classical modal logic. It gives a syntactic identication of a class of modal formulas whose associated normal modal logics are strongly complete with respect to elementary (i.e. rst-order denable)