Publications
154 results found
Brody DC, Hadjipetri S, 2015, COHERENT CHAOS INTEREST-RATE MODELS, INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, Vol: 18, ISSN: 0219-0249
Brody DC, Gibbons GW, Meier DM, 2015, Time-optimal navigation through quantum wind, NEW JOURNAL OF PHYSICS, Vol: 17, ISSN: 1367-2630
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- Citations: 41
Brody DC, Meier DM, 2015, Solution to the Quantum Zermelo Navigation Problem, PHYSICAL REVIEW LETTERS, Vol: 114, ISSN: 0031-9007
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- Citations: 36
Brody DC, Meier DM, 2015, Elementary solution to the time-independent quantum navigation problem, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 48, ISSN: 1751-8113
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- Citations: 13
Brody DC, Hughston LP, 2015, Universal Quantum Measurements, International Conference on Quantum Control, Exact or Perturbative, Linear or Nonlinear, Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588
Brody DC, 2014, Biorthogonal quantum mechanics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113
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- Citations: 236
Brody DC, 2013, Geometry of the complex extension of Wigner's theorem, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 46, ISSN: 1751-8113
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- Citations: 26
Brody DC, Graefe E-M, 2013, Information Geometry of Complex Hamiltonians and Exceptional Points, ENTROPY, Vol: 15, Pages: 3361-3378, ISSN: 1099-4300
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- Citations: 21
Brody DC, Hughston LP, 2013, Levy information and the aggregation of risk aversion, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 469, ISSN: 1364-5021
Bender CM, Brody DC, Caldeira J, et al., 2013, <i>PT</i>-symmetric quantum state discrimination, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 371, ISSN: 1364-503X
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- Citations: 25
Brody DC, Hughston LP, Yang X, 2013, Signal processing with Levy information, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 469, ISSN: 1364-5021
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- Citations: 7
Brody DC, Graefe E-M, 2012, Mixed-State Evolution in the Presence of Gain and Loss, PHYSICAL REVIEW LETTERS, Vol: 109, ISSN: 0031-9007
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- Citations: 96
Brody DC, Holm DD, Meier DM, 2012, Quantum splines, Physical Review Letters, Vol: 109, ISSN: 0031-9007
A quantum spline is a smooth curve parametrized by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm of the time rate of change of the associated Hamiltonian is minimized. The solution to the quantum spline problem is obtained, and is applied in an example that illustrates quantum control of coherent states. An efficient numerical scheme for computing quantum splines is discussed and implemented in the examples.
Brody DC, Hughston LP, Mackie E, 2012, General theory of geometric Levy models for dynamic asset pricing, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 468, Pages: 1778-1798, ISSN: 1364-5021
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- Citations: 17
Brody DC, Meister BK, Parry MF, 2012, Informational inefficiency in financial markets, MATHEMATICS AND FINANCIAL ECONOMICS, Vol: 6, Pages: 249-259, ISSN: 1862-9679
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- Citations: 2
Brody DC, Hughston LP, Macrina A, 2012, Information-based asset pricing, Finance at fields, Pages: 115-150, ISBN: 9789814407885
A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the corresponding price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such “X-factor” we associate a market information process, the values of which we assume are accessible to market participants. Each information process consists of a sum of two terms; one contains true information about the value of the associated market factor, and the other represents “noise”. The noise term is modelled by an independent Brownian bridge that spans the interval from the present to the time at which the value of the factor is revealed. The market filtration is assumed to be that generated by the aggregate of the independent information processes. The price of an asset is given by the expectation of the discounted cash flows in the risk neutral measure, conditional on the information provided by the market filtration. In the case where the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price process. Dividend growth is taken into account by introducing appropriate structure on the market factors. The prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European-style call option is of the Black-Scholes-Merton type. We consider the case where the rate at which information is revealed to the market is constant, and the case where the information rate varies in time. Option pricing formulae are obtained for both cases. The information-based framework generates a natural explanation for the origin of stochastic volatility in financial markets, without the need for specifying on an ad hoc basis the dynamics of the vola
Brody DC, Hughston LP, Mackie E, 2012, Rational term structure models with geometric Levy martingales, Publisher: TAYLOR & FRANCIS LTD
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- Citations: 2
Brody DC, Graefe E-M, 2011, Six-dimensional space-time from quaternionic quantum mechanics, PHYSICAL REVIEW D, Vol: 84, ISSN: 1550-7998
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- Citations: 11
Brody DC, Law YT, 2011, Theory of Information Pricing
In financial markets valuable information is rarely circulated homogeneously,because of time required for information to spread. However, advances incommunication technology means that the 'lifetime' of important information istypically short. Hence, viewed as a tradable asset, information shares thecharacteristics of a perishable commodity: while it can be stored andtransmitted freely, its worth diminishes rapidly in time. In view of recentdevelopments where internet search engines and other information providers areoffering information to financial institutions, the problem of pricinginformation is becoming increasingly important. With this in mind, a newformulation of utility-indifference argument is introduced and used as a basisfor pricing information. Specifically, we regard information as a quantity thatconverts a prior distribution into a posterior distribution. The amount ofinformation can then be quantified by relative entropy. The key to our utilityindifference argument is to equate the maximised a posterior utility, afterpaying certain cost for the information, with the a posterior expectation ofthe utility based on the a priori optimal strategy. This formulation leads toone price for a given quantity of upside information; and another price for agiven quantity of downside information. The ideas are illustrated by means ofsimple examples.
Brody DC, Graefe E, 2011, Coquaternionic quantum dynamics for two-level systems, Acta Polytechnica: journal of advanced engineering, Vol: 51, Pages: 14-20
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionicquantum theory is investigated. It is shown that the time evolution exhibitsthree different characteristics, depending on the values of the parameters ofthe Hamiltonian. When energy eigenvalues are real, the evolution is eitherisomorphic to that of a complex Hermitian theory on a spherical state space, orelse it remains unitary along an open orbit on a hyperbolic state space. Whenenergy eigenvalues form a complex conjugate pair, the orbit of the timeevolution closes again even though the state space is hyperbolic.
Brody DC, Hughston LP, Macrina A, 2011, Modelling information flows in financial markets, Advanced Mathematical Methods for Finance, Editors: Di Nunno, Oksendal, Nunno, Oksendal, Publisher: Springer Verlag, Pages: 133-153, ISBN: 9783642184116
, 2011, Preface, Rising Waters, Publisher: Cambridge University Press, Pages: vii-vii
Andruszkiewicz G, Brody DC, 2011, Noise, risk premium, and bubble
The existence of the pricing kernel is shown to imply the existence of anambient information process that generates market filtration. This informationprocess consists of a signal component concerning the value of the randomvariable X that can be interpreted as the timing of future cash demand, and anindependent noise component. The conditional expectation of the signal, inparticular, determines the market risk premium vector. An addition to thesignal of any term that is independent of X, which generates a drift in thenoise, is shown to change the drifts of price processes in the physicalmeasure, without affecting the current asset price levels. Such a drift in thenoise term can induce anomalous price dynamics, and can be seen to explain themechanism of observed phenomena of equity premium and financial bubbles.
Brody DC, Graefe E-M, 2011, On complexified mechanics and coquaternions, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 44, ISSN: 1751-8113
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- Citations: 43
Brody DC, Graefe EM, 2011, Coquaternionic quantum dynamics for two-level systems, Acta Polytechnica: journal of advanced engineering, Vol: 51, Pages: 14-20
Brody DC, 2011, Information geometry of density matrices and state estimation, J. Phys. A, Vol: 44
Brody DC, Hughston LP, Macrina A, 2010, Credit risk, market sentiment and randomly-timed default, Stochastic Analysis 2010, Editors: Crisan, Publisher: Springer Verlag, ISBN: 9783642153570
Brody DC, Law YT, 2010, Asset pricing with random information flow
In the information-based approach to asset pricing the market filtration ismodelled explicitly as a superposition of signals concerning relevant marketfactors and independent noise. The rate at which the signal is revealed to themarket then determines the overall magnitude of asset volatility. By lettingthis information flow rate random, we obtain an elementary stochasticvolatility model within the information-based approach. Such an extension iseconomically justified on account of the fact that in real markets informationflow rates are rarely measurable. Effects of having a random information flowrate is investigated in detail in the context of a simple model setup.Specifically, the price process of the asset is derived, and its characteristicbehaviours are revealed via simulation studies. The price of a European-styleoption is worked out, showing that the model has a sufficient flexibility tofit volatility surface. As an extension of the random information flow model,price manipulation is considered. A simple model is used to show how theskewness of the manipulated and unmanipulated price processes take oppositesignature.
Brody DC, Brody J, Meister BK, et al., 2010, Outsider Trading
In this paper we examine inefficiencies and information disparity in theJapanese stock market. By carefully analysing information publicly available onthe internet, an `outsider' to conventional statistical arbitragestrategies--which are based on market microstructure, company releases, oranalyst reports--can nevertheless pursue a profitable trading strategy. A largevolume of blog data is used to demonstrate the existence of an inefficiency inthe market. An information-based model that replicates the trading strategy isdeveloped to estimate the degree of information disparity.
Bender CM, BRODY D, 2010, Optimal time evolution for Hermitian and non-Hermitian Hamiltonians, Time in Quantum Mechanics, Editors: Muga, Ruschhaupt, Campo, Publisher: Springer Verlag, ISBN: 9783642031731
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