42 research outputs found
The kind of silence: managing a reputation for voluntary disclosure in financial markets
No full textWe create a continuous-time setting in which to investigate how the management of a firm controls a dynamic choice between two generic voluntary disclosure decision rules (strategies) in the period between two consecutive mandatory disclosure dates: one with full and transparent disclosure termed candid, the other, termed sparing, under which values only above a dynamic threshold are disclosed. We show how parameters of the model such as news intensity, pay-for-performance and time-to-mandatory-disclosure determine the optimal choice of candid versus sparing strategies and the optimal times for management to switch between the two. The model presented develops a number of insights, based on a very simple ordinary differential equation characterizing equilibrium in a piecewise-deterministic model, derivable from the background Black-Scholes model and Poisson arrival of signals of firm value. It is shown that in equilibrium when news intensity is low a firm may employ a candid disclosure strategy throughout, but will otherwise switch (alternate) between periods of being candid and periods of being sparing with the truth (or the other way about). Significantly, with constant pay-for-performance parameters, at most one switching can occur
The sound of silence: equilibrium filtering and optimal censoring in financial markets
No full textFollowing the approach of standard filtering theory, we analyse investor valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold their observations; explicit filtering formulae are derived for downgrading the valuations in the absence of disclosures. The analysis is conducted for both a solitary firm and m co-dependent firms
Homomorphisms from functional equations: The Goldie equation, II
No full textThis first of three sequels to Homomorphisms from Functional equations: The Goldie equation (Ostaszewski in Aequationes Math 90:427–448, 2016) by the second author—the second of the resulting quartet—starts from the Goldie functional equation arising in the general regular variation of our joint paper (Bingham et al. in J Math Anal Appl 483:123610, 2020). We extend the work there in two directions. First, we algebraicize the theory, by systematic use of certain groups—the Popa groups arising in earlier work by Popa, and their relatives the Javor groups. Secondly, we extend from the original context on the real line to multi-dimensional (or infinite-dimensional) settings
Regular variation, tological dynamics, and the uniform boundedness theorem
No full textIn the metrizable topological groups context, a semi-direct product construction provides a canonical multiplicative representation for arbitrary continuous flows. This implies, modulo metric differences, the topological equivalence of the natural flow formalization of regular variation of N. H. Bingham and A. J. Ostaszewski in [Topological regular variation: I. Slow variation, [to appear in Topology and its Applications]with the B. Bajsanski and J. Karamata group formulation in [Regularly varying functions and the principle of egui-continuity, Publ. Ramanujan Inst. 1 (1968/1969), 235-246]. In consequence, topological theorems concerning subgroup actions may be lifted to the flow setting. Thus, the Bajsanski-Karamata Uniform Boundedness Theorem (UBT), as it applies to cocycles in the continuous and Baire cases, may be reformulated and refined to hold under Baire-style Caratheodory conditions. Its connection to the classical UBT, due to Stefan Banach and Hugo Steinhaus, is clarified. An application to Banach algebras is given
‘Equity smirks ’ and embedded options: the shape of a firm’s value function
No full textThis 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 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 hypergeometric functions associated with the Merton-style valuation equation 1 2 ζη d2V dV + (r − q)η − rV = 0. dη2 dη 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 snakelike 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) 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 α is made. This is the full, detailed, version of a discussion paper presented a
Freezing in Space-time: A functional equation linked with a PDE system
No full textWe analyze the functional equation and reveal its
relationship with a system of partial differential equations arising as the
hydrodynamic limit of a system of pinned billiard balls on the line. The system
of balls must freeze at some time, i.e., no velocity may change after the
freezing time. The terminal velocity and the freezing time profiles play the
role of boundary conditions for the PDEs (qua terminal conditions, despite
being initial conditions from the wave equation perspective pursued here).
Solutions to the functional equation provide the link between the freezing time
and terminal velocity profiles on the one hand, and the solution to the PDE in
the entirety of the space-time domain on the other.Comment: Metadata typos correcte
Homomorphisms from functional equations: the Goldie equation
No full textThe theory of regular variation, in its Karamata and Bojani´c-Karamata/de Haan forms, is long established and makes essential use of the Cauchy functional equation. Both forms are subsumed within the recent theory of Beurling regular variation, developed elsewhere. Various generalizations of the Cauchy equation, including the Gołab–Schinzel functional equation (GS) and Goldie's equation (GBE) below, are prominent there. Here we unify their treatment by algebraicization: extensive use of group structures introduced by Popa and Javor in the 1960s turn all the various (known) solutions into homomorphisms, in fact identifying them 'en passant', and show that (GS) is present everywhere, even if in a thick disguise
Returns to costly pre-bargaining claims: Taking a principled stand
No full textWe construct a ‘divide the dollar’bargaining game which formalizes Schelling’s notion of a ‘qualitative commitment’. This requires a substantial capitulation cost to be incurred – discontinuously –if and only if a player accepts a share of an asset below his pre-announced ‘claim’on it, no matter how little below. The ‘commitment game’opens with an ‘announcement round ’ in which the two players simultaneously announce their claims on the asset, and is followed by a Rubinstein alternating-o¤ers ‘negotiation subgame’. We determine the unique subgame-perfect, stationary, pure-strategy equilibrium outcome of the commitment game and …nd it to be e ¢ cient. The main feature of the model is that gains, relative to the game without commitment, do result to the …rst-mover provided the capitulation cost is above a certain threshold. The more the capitulation cost exceeds the threshold, the greater is the gain. The higher the impatience level of the players, the higher the stakes need to be. It is a pleasure to o¤er thanks to John Sutton, John Hardiman Moore, Ken Binmore and Bernhard von Stengel for discussions, as well as to Michael Schroeder for invaluable services as a patient reader, and to the anonymous referees for prompting a number of interesting questions that have led to improvements to the main thrust of this paper
