164,377 research outputs found
Predictable arguments of knowledge
We initiate a formal investigation on the power of predictability for argument of knowledge systems for NP. Specifically, we consider private-coin argument systems where the answer of the prover can be predicted, given the private randomness of the verifier; we call such protocols Predictable Arguments of Knowledge (PAoK).
Our study encompasses a full characterization of PAoK, showing that such arguments can be made extremely laconic, with the prover sending a single bit, and assumed to have only one round (i.e., two messages) of communication without loss of generality.
We additionally explore PAoK satisfying additional properties (including zero-knowledge and the possibility of re-using the same challenge across multiple executions with the prover), present several constructions of PAoK relying on different cryptographic tools, and discuss applications to cryptography
(Commit-and-Prove) Predictable Arguments with Privacy
Predictable arguments introduced by Faonio, Nielsen and Venturi (PKC17) are private-coin argument systems where the answer of the prover can be predicted in advance by the verifier. In this work, we study predictable arguments with additional privacy properties. While the authors in [PKC17] showed compilers for transforming PAs into PAs with zero-knowledge property, they left the construction of witness indistinguishable predictable arguments (WI-PA) in the plain model as an open problem. In this work, we first propose more efficient constructions of zero-knowledge predictable arguments (ZK-PA) based on trapdoor smooth projective hash functions (TSPHFs). Next, we consider the problem of WI-PA construction in the plain model and show how to transform PA into WI-PA using non-interactive witness-indistinguishable proofs.
As a relaxation of predictable arguments, we additionally put forth a new notion of predictability called Commit-and-Prove Predictable Argument (CPPA), where except the first (reusable) message of the prover, all the prover’s responses can be predicted. We construct an efficient zero-knowledge CPPA in the non-programmable random oracle model for the class of all polynomial-size circuits. Finally, following the connection between predictable arguments and witness encryption, we show an application of CPPAs with privacy properties to the design of witness encryption schemes, where in addition to standard properties, we also require some level of privacy for the decryptors who own a valid witness for the statement used during the encryption process
Information, no-arbitrage and completeness for asset price models with a change point
We consider a general class of continuous asset price models where the drift
and the volatility functions, as well as the driving Brownian motions, change
at a random time . Under minimal assumptions on the random time and on
the driving Brownian motions, we study the behavior of the model in all the
filtrations which naturally arise in this setting, establishing martingale
representation results and characterizing the validity of the NA1 and NFLVR
no-arbitrage conditions.Comment: 21 page
Against Inefficacy Objections: The Real Economic Impact of Individual Consumer Choices on Animal Agriculture
When consumers choose to abstain from purchasing meat, they face some uncertainty about whether their decisions will have an impact on the number of animals raised and killed. Consequentialists have argued that this uncertainty should not dissuade consumers from a vegetarian diet because the “expected” impact, or average impact, will be predictable. Recently, however, critics have argued that the expected marginal impact of a consumer change is likely to be much smaller or more radically unpredictable than previously thought. This objection to the consequentialist case for vegetarianism is known as the “causal inefficacy” (or “causal impotence”) objection. In this paper, we argue that the inefficacy objection fails. First, we summarize the contours of the objection and the standard “expected impact” response to it. Second, we examine and rebut two contemporary attempts (by Mark Budolfson and Ted Warfield) to defeat the expected impact reply through alleged demonstrations of the inefficacy of abstaining from meat consumption. Third, we argue that there are good reasons to believe that single individual consumers—not just individual consumers taken as an aggregate—really do make a positive difference when they choose to abstain from meat consumption. Our case rests on three economic observations: (i) animal producers operate in a highly competitive environment, (ii) complex supply chains efficiently communicate some information about product demand, and (iii) consumers of plant-based meat alternatives have positive consumption spillover effects on other consumers
The Shannon information of filtrations and the additional logarithmic utility of insiders
The background for the general mathematical link between utility and
information theory investigated in this paper is a simple financial market
model with two kinds of small traders: less informed traders and insiders,
whose extra information is represented by an enlargement of the other agents'
filtration. The expected logarithmic utility increment, that is, the difference
of the insider's and the less informed trader's expected logarithmic utility is
described in terms of the information drift, that is, the drift one has to
eliminate in order to perceive the price dynamics as a martingale from the
insider's perspective. On the one hand, we describe the information drift in a
very general setting by natural quantities expressing the probabilistic better
informed view of the world. This, on the other hand, allows us to identify the
additional utility by entropy related quantities known from information theory.
In particular, in a complete market in which the insider has some fixed
additional information during the entire trading interval, its utility
increment can be represented by the Shannon information of his extra knowledge.
For general markets, and in some particular examples, we provide estimates of
maximal utility by information inequalities.Comment: Published at http://dx.doi.org/10.1214/009117905000000648 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
From the decompositions of a stopping time to risk premium decompositions
We build a general model for pricing defaultable claims. In addition to the
usual absence of arbitrage assumption, we assume that one defaultable asset (at
least) looses value when the default occurs. We prove that under this
assumption, in some standard market filtrations, default times are totally
inaccessible stopping times; we therefore proceed to a systematic construction
of default times with particular emphasis on totally inaccessible stopping
times. Surprisingly, this abstract mathematical construction, reveals a very
specific and useful way in which default models can be built, using both market
factors and idiosyncratic factors. We then provide all the relevant
characteristics of a default time (i.e. the Az\'ema supermartingale and its
Doob-Meyer decomposition) given the information about these factors. We also
provide explicit formulas for the prices of defaultable claims and analyze the
risk premiums that form in the market in anticipation of losses which occur at
the default event. The usual reduced-form framework is extended in order to
include possible economic shocks, in particular jumps of the recovery process
at the default time. This formulas are not classic and we point out that the
knowledge of the default compensator or the intensity process is not anymore a
sufficient quantity for finding explicit prices, but we need indeed the Az\'ema
supermartingale and its Doob-Meyer decomposition
Emergentism and musicology: an alternative perspective to the understanding of dissonance.
In this paper we develop an approach to musicology within the
discussion of emergentism. First of all, we claim that some theories of
musicology could be insufficient in describing and explaining musical
phenomena when emergent properties are not taken into account. Actually,
musicology usually considers just syntactical elements, structures and
processes and puts only a little emphasis, if any, over perceptual aspects of
human hearing. On the other hand, recent research efforts are currently being
directed towards an understanding of the emergent properties of auditory
perception, especially in fields such as cognitive science. Such research leads
to other views concerning old issues in musicology and could create a fruitful
approach, filling the gap between musicology and auditory perception
On arbitrages arising from honest times
In the context of a general continuous financial market model, we study
whether the additional information associated with an honest time gives rise to
arbitrage profits. By relying on the theory of progressive enlargement of
filtrations, we explicitly show that no kind of arbitrage profit can ever be
realised strictly before an honest time, while classical arbitrage
opportunities can be realised exactly at an honest time as well as after an
honest time. Moreover, stronger arbitrages of the first kind can only be
obtained by trading as soon as an honest time occurs. We carefully study the
behavior of local martingale deflators and consider no-arbitrage-type
conditions weaker than NFLVR.Comment: 25 pages, revised versio
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