## Publications

156 results found

Bender CM, Brody DC, 2019, Operator-valued zeta functions and Fourier analysis, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 52, ISSN: 1751-8113

Brody DC, 2018, Biorthogonal systems on unit interval and zeta dilation operators, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 51, ISSN: 1751-8113

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- Citations: 1

Brody DC, Hughston LP, Meier DM, 2018, Lévy-Vasicek models and the long-bond return process, ISSN: 0219-0249

© 2018 World Scientific Publishing Company. The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Lévy-Vasicek case, avoiding issues of market incompleteness. In the Lévy-Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Lévy driver admitting exponential moments. Expressions are obtained for the Lévy-Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by Lt =limT→∞PtT/P0T, where PtT is the price at time t of a T-maturity discount bond. We show that the pricing kernel of a Lévy-Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

Bender CM, Brody DC, 2018, Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 51, ISSN: 1751-8113

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- Citations: 3

Brody DC, Hughston LP, 2018, SOCIAL DISCOUNTING AND THE LONG RATE OF INTEREST, *MATHEMATICAL FINANCE*, Vol: 28, Pages: 306-334, ISSN: 0960-1627

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- Citations: 2

Brody DC, 2017, PT-symmetry, indefinite metric, and nonlinear quantum mechanics, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 50, ISSN: 1751-8113

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- Citations: 1

Bender CM, Brody DC, Mueller MP, 2017, Hamiltonian for the Zeros of the Riemann Zeta Function, *PHYSICAL REVIEW LETTERS*, Vol: 118, ISSN: 0031-9007

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- Citations: 26

Brody DC, Hughston LP, 2016, Thermodynamics of quantum heat bath, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 49, ISSN: 1751-8113

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- Citations: 1

Brody DC, Gibbons GW, Meier DM, 2016, A Riemannian approach to Randers geodesics, *JOURNAL OF GEOMETRY AND PHYSICS*, Vol: 106, Pages: 98-101, ISSN: 0393-0440

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- Citations: 4

Brody DC, 2016, Consistency of PT-symmetric quantum mechanics, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 49, ISSN: 1751-8113

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- Citations: 20

Bender CM, Brody DC, Hughston LP, et al., 2016, Geometric Aspects of Space-Time Reflection Symmetry in Quantum Mechanics, 15th International Workshop on Pseuso-Hermitian Hamiltonians in Quantum Physics (PHHQP), Publisher: SPRINGER-VERLAG BERLIN, Pages: 185-199, ISSN: 0930-8989

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- Citations: 1

Brody DC, Hughston LP, Meier DM, 2015, Fragile entanglement statistics, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 48, ISSN: 1751-8113

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: 16

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: 17

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: 9

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, Law YT, 2015, Pricing of Defaultable Bonds with Random Information Flow, *Applied Mathematical Finance*, Vol: 22, Pages: 399-420, ISSN: 1350-486X

© 2015 Taylor & Francis. In the information-based approach to asset pricing, the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market then determines the overall magnitude of asset volatility. By letting this information flow rate random, we obtain an elementary stochastic volatility model within the information-based approach. Such an extension is justified on account of the fact that in real markets information flow rates are rarely measurable. Effects of having a random information flow rate are investigated in detail in the context of a simple model setup. Specifically, the price process of an elementary defaultable bond is derived, and its characteristic behaviours are revealed via simulation studies. The price of a European-style option on the bond is worked out, showing that the model has a sufficient flexibility to fit volatility surface. As an extension of the random information flow model, modelling of price manipulation is considered. A simple model is used to show how the skewness of the manipulated and unmanipulated price processes take opposite signature.

Brody DC, 2014, Biorthogonal quantum mechanics, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 47, ISSN: 1751-8113

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- Citations: 56

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: 8

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: 13

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, PT-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: 9

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: 3

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: 37

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: 13

Brody DC, Meister BK, Parry MF, 2012, Informational inefficiency in financial markets, *Mathematics and Financial Economics*, Vol: 6, Pages: 249-259, ISSN: 1862-9679

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 information-based model that approximately replicates the strategy is developed to estimate the degree of information disparity. The result shows that an efficient internet search engine can considerably enhance market efficiency, as measured in terms of the information flow rate. © 2012 Springer-Verlag.

Brody DC, Hughston LP, Mackie E, 2012, Rational term structure models with geometric Levy martingales, Publisher: TAYLOR & FRANCIS LTD

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- Citations: 1

Brody DC, Hughston LP, Macrina A, 2012, Information-based asset pricing, Finance at fields, Pages: 115-150, ISBN: 9789814407885

© 2013 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. 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 market

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