Bernhard K. Meister

Renmin University of China | RUC

The gas fee, paid for inclusion in the blockchain, is analyzed in two parts. First, we consider how effort in terms of resources required to process and store a transaction turns into a gas limit, which, through a fee, comprised of the base and priority fee in the current version of Ethereum, is converted into the cost paid by the user. We hew clos...

A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is accrued through astute betting. As information is gained from the stream of particles, the measurement directions...

Myopic investors are locally rational decision-makers but globally irrational. Their suboptimal portfolios lag the market. As a consequence, other market participants are provided with profit opportunities. Not subterfuge but constrained optimisation leads to disparities. Four overlapping examples are given. The first case centres on the difference...

A quantum algorithm is presented for distinguishing between candidate functions, which are all defined on the same finite set, map each element except one to zero, and are uniquely identified by the single element mapped to one. An observable created out of components, including a hermitian operator mimicking the oracle employed in the unstructured...

On the blockchain, NFT games have risen in popularity, spawning new types of digital assets. We present a simplified version of well-known NFT games, followed by a discussion of issues influencing the structure and stability of generic games. Where applicable, ideas from quantitative finance are incorporated, suggesting various design constraints....

Investors trade shifting prices, portfolio values, and in turn their ability to borrow. Concentrated ownership, high price impact and low collateral requirements are propitious for arbitrage.

The paper highlights some commonalities between the development of cryptocurrencies and the evolution of ecosystems. Concepts from evolutionary finance embedded in toy models consistent with stylized facts are employed to understand what survival of the fittest means in cryptofinance. Stylized facts for ownership, trading volume and market capitali...

In this chapter structures that generate yield in cryptofinance will be analyzed and related to leverage. While the majority of crypto-assets do not have intrinsic yields in and of themselves, similar to cash holdings of fiat currency, revolutionary innovation based on smart contracts, which enable decentralised finance, does generate return. Examp...

A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits functional degrees of freedom that can...

A discretized version of the adiabatic theorem is described with the help of a rule relating a Hermitian operator to its expectation value and variance. The simple initial operator X with known ground state is transformed in a series of N small steps into a more complicated final operator Z with unknown ground state. Each operator along the discret...

A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically enlarged. At specific, periodically recurring, times the particle can be found with probability one at the oppo...

The influence of Commodity Trading Advisors (CTA) on the price process is explored with the help of a simple model. CTA managers are taken to be Kelly optimisers, which invest a fixed proportion of their assets in the risky asset and the remainder in a riskless asset. This requires regular adjustment of the portfolio weights as prices evolve. The C...

Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a particle can change its energy, as it gets entangled with the barriers and the insertion points become nodes. Two...

Quantum state discrimination between two wave functions on a ring is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting instantaneously two impenetrable barriers dividing the ring into two chambers. In the process, the candidate wave functions, as the insertion poi...

For nearly two decades, much research has been carried out on properties of physical systems described by Hamiltonians that are not Hermitian in the conventional sense, but are symmetric under space-time reflection; that is, they exhibit \(\mathscr {PT}\) symmetry. Such Hamiltonians can be used to model the behavior of closed quantum systems, but t...

State discrimination with the aim to minimize the error probability is a well studied problem. Instead, here the binary decision problem for operators with a given prior is investigated. A black box containing the unknown operator is probed by selected wave functions. The output is analyzed with conventional methods developed for state discriminati...

The objective of this paper is to explain and elucidate the formalism of quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ1〉 or |ψ2〉. If these states are not orthogonal, then the requi...

The existence of an informational inefficiency in the equity market is identified by analysing information publicly available on the internet. A large volume of blog data is used for this purpose. Informational inefficiency is established by converting company-specific blog sentiment data into a trading strategy and analysing its performance. An in...

The problem of quantum state discrimination between two wave functions with fixed prior is considered. The optimal minimum-error probability for the state discrimination is known to be given by the Helstrom bound. A new strategy is introduced here whereby a series of 'negative-result experiments' a la Renninger is carried out to modify the wave fun...

The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting an impenetrable barrier in the middle of the square well, which is either a nodal or non-nodal poin...

Suppose that a system is known to be in one of two quantum states, $|\psi_1 > $ or $|\psi_2 >$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner prod...

In this paper we examine inefficiencies and information disparity in the Japanese stock market. By carefully analysing information publicly available on the internet, an `outsider' to conventional statistical arbitrage strategies--which are based on market microstructure, company releases, or analyst reports--can nevertheless pursue a profitable tr...

We study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio in terms of drift, short term risk-free rate and co...

The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability for the state discrimination is known to be given by the Helstrom bound. A new strategy is introduced here whereby the square well is compressed isoenergetically, modifying the wave-fun...

In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a set of price processes satisfy...

In this brief comment we attempt to clarify the apparent discrepancy between the papers [1] and [2] on the quantum brachistochrone, namely whether it is possible to use a judicious mixture of Hermitian and non-Hermitian quantum mechanics to evade the standard lower limit on the time taken for evolution by a Hermitian Hamiltonian with given energy d...

Every maturity-dependent derivative contract entails a term structure. For example, when the value of the portfolio consisting of a long position in a stock and a short position in a vanilla option is expressed in units of its instantaneous exercise value, the resulting quantity defines a discount function. Thus, the derivative of the discount func...

The Lüders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar spin-$\frac{1}{2}$ particle observables is described and implementation issues are briefly analyzed.

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum information processing. Here, we inve...

Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem associated with such Hamiltonians have shown that in many cases the entire energy spectrum is real and positive an...

An extension of the Wigner-Araki-Yanase theorem to multiplicative conserved quantities is presented and approximate versions of the theorem are discussed.

Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation...

For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph theory.

The Luders postulate is reviewed and implications for quantum algorithms are discussed. A search algorithm for an unstructured database is described.

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.

The entropic calibration of the risk-neutral density function is effective in recovering the strike dependence of options, but encounters difficulties in determining the relevant greeks. By use of put-call reversal we apply the entropic method to the time reversed economy, which allows us to obtain the spot price dependence of options and the relev...

This paper analyses the mathematical properties of some unusual quantum states that are constructed by inserting an impenetrable barrier into a chamber confining a single particle. If the barrier is inserted at a fixed node of the wave function, then the energy of the system is unchanged. After barrier insertion, a measurement is made on one side o...

The second partial derivative of a European-style vanilla option with respect to the current price of the underlying asset—the option gamma—defines a probability density function for the current underlying price. By use of entropy maximization it is possible to obtain an option gamma, from which the associated option pricing formula can be recovere...

This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical mechanics in which a beam is supported by three identical rigid pillars. For this problem it is not possible to calcu...

A formula for the Taylor series expansion of the rth power of the modified Bessel function I (z) r is derived for arbitrary r. The result is expressed in terms of a recursive formula for a class of polynomials, which facilitates the systematic con-struction of the expansion of I (z) r . © 2003 American Institute of Physics.

It is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of...

A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum mechanical particle confined to a potential well. The efficiency...

We consider a general model for an investment producing a single commodity, and, assuming that there exists a traded asset spanning the corresponding market, we prove a "verification theorem" which relates the solution of an appropriate differential equation with the investment's contingent claim price. In this way, we show in a mathematically rigo...

Generalized uncertainty relations based upon Fourier transforms of both discrete and continuous functions are briefly reviewed. We extend these results in order to establish discrete versions of the angular momentum uncertainty relations, based upon SU(2) transformations. Possible applications in quantum signal processing and computations are brief...

Given a sequence of numbers {a(n)}, it is always possible to find a set of Feynman rules that reproduce that sequence. For the special case of the partitions of the integers, the appropriate Feynman rules give rise to graphs that represent the partitions in a clear pictorial fashion. These Feynman rules can be used to generate the Bell numbers B(n)...

A general model for the valuation of natural resource investments is formulated and analyzed within a stochastic control theoretic framework. Using dynamic programming, the value of such an investment with a general payoff function is determined under the assumption that the commodity price process is given by a stochastic differential equation. Th...

A general model for the valuation of an investment producing a single commodity is formulated and analysed within a stochastic control theoretic framework. Using dynamic programming, the value of such an investment with a general payoff function is determined under the assumption that the commodity price process is given by a stochastic differentia...

Generalised uncertainty relations based upon Fourier transforms of discrete func-tions are reviewed. A new discrete version of the angular momentum uncertainty relations, based upon SU(2) transformations, is proved. Possible applications in quantum signal processing are also discussed.

Thesis (Ph. D.)--University of London, 1996.

For a given ensemble of $N$ independent and identically prepared particles, we calculate the binary decision costs of different strategies for measurement of polarised spin 1/2 particles. The result proves that, for any given values of the prior probabilities and any number of constituent particles, the cost for a combined measurement is always les...

Bayes criteria are explicitly applied to statistical decision problems in simple quantum mechanical systems. The minimum Bayes cost is calculated for systems including polarised spins and relativistic spin 12 particles. The results suggest that, in decisions for a given ensemble of particles, on the average, the Bayes cost almost always decreases i...

For any irreversible system, classical or quantum mechanical, the time derivative of the entropy is always positive. Recently, an upper bound for the time derivative of the Shannon entropy was obtained. In the present paper, an alternative form of the bound is derived and applied to obtain an upper bound for entropy production.

In this paper alternative formulations of the conventional uncertainty relation are studied in the context of decoherent histories. The results are given in terms of Shannon information. A variety of methods are developed to evaluate the upper bound for the probability of two or more projection histories. The methods employed give improved limits f...