Adam Ostaszewski

Kingman, category and combinatorics

Focussing on the work of Sir John Kingman, one of the worlds leading researchers in probability and mathematical genetics, this book touches on the important areas of these subjects in the last 50 years. Leading authorities give a unique insight into a wide range of currently topical problems. Papers in probability concentrate on combinatorial and structural aspects, in particular exchangeability and regeneration. The Kingman coalescent links probability with mathematical genetics and is fundamental to the study of the latter. This has implications across the whole of genomic modelling including the Human Genome Project. Other papers in mathematical population genetics range from statistical aspects including heterogeneous clustering, to the assessment of molecular variability in cancer genomes. Further papers in statistics are concerned with empirical deconvolution, perfect simulation, and wavelets. This book will be warmly received by established experts as well as their students and others interested in the content.

Dichotomy and infinite combinatorics: the theorems of Steinhaus and Ostrowski

We define combinatorial principles which unify and extend the classical results of Steinhaus and Piccard on the existence of interior points in the distance set. Thus the measure and category versions are derived from one topological theorem on interior points applied to the usual topology and the density topology on the line. Likewise we unify the subgroup theorem by reference to a Ramsey property. A combinatorial form of Ostrowskis theorem (that a bounded additive function is linear) permits the deduction of both the measure and category automatic continuity theorems for additive functions.

A note on the Prabir Roy space

Abstract A modification is given of the Prabir Roy construction of a zero-dimensional complete metric space which is not strongly zero-dimensional and which has weight ℵ1. A generalisation is offered to encompass a similar recent construction due to Kulesza.

Effros, Baire, Steinhaus and non-separability

We give a short proof of an improved version of the Effros Open Mapping Principle via a shift-compactness theorem (also with a short proof), involving ‘sequential analysis’ rather than separability, deducing it from the Baire property in a general Baire-space setting (rather than under topological completeness). It is applicable to absolutely-analytic normed groups (which include complete metrizable topological groups), and via a Steinhaus-type Sum-set Theorem (also a consequence of the shift-compactness theorem) includes the classical Open Mapping Theorem (separable or otherwise).

Dividend Policy Irrelevancy and the Construct of Earnings

This paper analyzes the characteristics of earnings in valuation settings where the dividend policy is irrelevant to equity value. The paper first demonstrates an equivalent characterization of dividend policy irrelevancy (DPI) in a general linear dynamic. It then proceeds to show how DPI leads to ideal and practical constructs of earnings and examines their analytical properties. We further demonstrate that earnings properties can be used to deduce the core approach in practical equity valuation – namely, measures of growth in expected earnings explain the price to forward earnings ratio. However, unlike dividends, free cash flow cannot generally be claimed to be irrelevant to value.

Why managers with low forecast precision select high disclosure intensity: an equilibrium analysis

Shin (2006) has argued that in order to understand the equilibrium patterns of corporate disclosure, it is necessary for researchers to work within an asset pricing framework in which corporate disclosures are endogenously determined. Echoing this sentiment, Larcker and Rusticus (2010) have argued that earlier empirical results claiming to find a negative relationship between disclosure and cost of capital may suffer fatally from endogeneity issues which, once addressed by a formal structural model, may reverse the sign of the relationship. The purpose of this paper is to introduce a general equilibrium model following the Black-Scholes paradigm with endogeneous disclosure in which firms select uniquely determined optimal probabilities of early equity-value discovery in a noisy environment. As firms may differ also in the uncertainty (precision) with which management can forecast the future, managers strategically increase the intensity of their (voluntary) disclosures to provide partial compensation for this perceived differential risk. A positive relationship then results between disclosure and the cost of capital.

Equity smirks and embedded options: the shape of a firm's value function

Abstract This paper examines the methodology and assumptions of Ashton, D., Cooke, T., Tippett, M., Wang, P. (2004) employing recursion value η as an explanatory single-variable in a model of the firm, first introduced by Ashton, D., Cooke, T., Tippett, M., in (2003). A qualitative analysis of all of their numerical findings is given together with an indication of how more useful is the tool of special function theory, here requiring confluent hyper-geometric functions associated with the Merton-style valuation equation A justification and a wider interpretation of their model and findings is offered: these come from inclusion of strictly convex dissipating frictions arising either as insurance costs, replacement costs of funds paid out, or of debt service, and from the inclusion of alternative adaptation options embedded in the equity value of a firm; these predict not only a J-shaped equity curve, but also, under the richer modelling assumption, a snake-like curve that may result from financial frictions like insurance. These ‘smirks’ in the equity curve may be empirically tested. It is shown that the inclusion of frictions in dividend selection (e.g. the signalling costs of Bhattacharya, 1979) leads to an optimal dividend payout of αη that is a constant coupon for an interval of η values preceded by an interval in which α = r; this is at variance with the ACTW model where the exogeneous assumption of a constant a is made.

Optimal Disbursement of a Sunk Resource and Decentralised Cost Allocation

Abstract We consider whether the allocation of the sunk cost of a central resource to operating divisions can be consistent with economically optimal resource consumption decisions. When it is recognised that the central resource is scarce, one may, in principle, defend the allocation of sunk cost, if it measures the opportunity cost of usage. However, typically it has been proposed that such allocations are, at best, a proxy for opportunity cost. Applying classical control theory techniques in a wide range of operating environments, we are able to identify cost allocations that exactly equal opportunity cost. Hence, for our model environment, we provide a rationale for sunk cost allocation in terms of guiding optimal decisions, in contrast to the traditional defence in terms of providing a proxy for opportunity cost. We demonstrate clearly how cost allocations are related to opportunity costs, and identify the circumstances under which the allocation of full costs or alternatively a fixed proportion (rel...

Predicting firm value: the superiority of q-theory over residual income

Abstract One of the contributions of residual income theory is that it establishes an equivalence between valuation of a firm based upon a discounted stream of future dividends and valuation based on accounting data in which book value and a discounted stream of future residual incomes take centre stage. However, this equivalence result is non-unique: residual income is only one of many income measures for which equivalence can be shown to hold. Given this non-uniqueness, the traditional residual income equivalence result provides at best a weak defence for the necessity of accounting via residual income. The principal objective of the current paper is to address this central limitation of existing research. We consider how to move on from dependence on equivalence as a weak defence for accounting-based valuation, to a framework in which strict preference between alternative valuation methods is possible. The principal reason why previous research has not considered such issues is because it has lacked an underlying microeconomic theory of managerial choice providing a framework within which to rank alternative valuation rules. From first principles we develop a dynamic optimisation model of managerial choice that provides the benchmark by which we can objectively appraise valuation based upon residual and other income measures. We show that hysteresis (non-uniqueness of valuation) can typically arise for residual income, whereas in contrast for the q-theory based income measure which we derive, valuation is, as expected intuitively, increasing in income (under some mild regularity conditions). Furthermore, we show how our proposed g-theory income measure could be estimated empirically and that our model provides an explanation for some of the apparent anomalies in the Burgstahler-Dichev empirical findings.

Set theory and the analyst

This survey is motivated by specific questions arising in the similarities and contrasts between (Baire) category and (Lebesgue) measure—category-measure duality and non-duality, as it were. The bulk of the text is devoted to a summary, intended for the working analyst, of the extensive background in set theory and logic needed to discuss such matters: to quote from the preface of Kelley (General Topology, Van Nostrand, Toronto, 1995): “what every young analyst should know”.