|   | 
Details
   web
Records
Author (up) Aros, R.; Contreras, M.
Title Torsion induces gravity Type
Year 2006 Publication Physical Review D Abbreviated Journal Phys. Rev. D
Volume 73 Issue 8 Pages 4 pp
Keywords
Abstract In this work the Poincare-Chern-Simons and anti-de Sitter-Chern-Simons gravities are studied. For both, a solution that can be cast as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions, respectively.
Address Univ Andres Bello, Dept Cinemas Fis, Santiago, Chile
Corporate Author Thesis
Publisher American Physical Soc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1550-7998 ISBN Medium
Area Expedition Conference
Notes WOS:000237159600093 Approved
Call Number UAI @ eduardo.moreno @ Serial 43
Permanent link to this record
 

 
Author (up) Bustamante, M.; Contreras, M.
Title Multi-asset Black-Scholes model as a variable second class constrained dynamical system Type
Year 2016 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 457 Issue Pages 540-572
Keywords Multiasset Black-Scholes equation; Option pricing; Singular Lagrangian systems; Dirac's method; Propagators; Constrained Hamiltonian path integrals
Abstract In this paper, we study the multi-asset Black-Scholes model from a structural point of view. For this, we interpret the multi-asset Black-Scholes equation as a multidimensional Schrodinger one particle equation. The analysis of the classical Hamiltonian and Lagrangian mechanics associated with this quantum model implies that, in this system, the canonical momentums cannot always be written in terms of the velocities. This feature is a typical characteristic of the constrained system that appears in the high-energy physics. To study this model in the proper form, one must apply Dirac's method for constrained systems. The results of the Dirac's analysis indicate that in the correlation parameters space of the multi assets model, there exists a surface (called the Kummer surface Sigma(K), where the determinant of the correlation matrix is null) on which the constraint number can vary. We study in detail the cases with N = 2 and N = 3 assets. For these cases, we calculate the propagator of the multi-asset Black-Scholes equation and show that inside the Kummer Sigma(K) surface the propagator is well defined, but outside Sigma(K) the propagator diverges and the option price is not well defined. On Sigma(K) the propagator is obtained as a constrained path integral and their form depends on which region of the Kummer surface the correlation parameters lie. Thus, the multi-asset Black-Scholes model is an example of a variable constrained dynamical system, and it is a new and beautiful property that had not been previously observed. (C) 2016 Elsevier B.V. All rights reserved.
Address [Bustamante, M.; Contreras, M.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000376693600051 Approved
Call Number UAI @ eduardo.moreno @ Serial 631
Permanent link to this record
 

 
Author (up) Contreras, M.; Echeverria, J.; Pena, J.P.; Villena, M.
Title Resonance phenomena in option pricing with arbitrage Type
Year 2020 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 540 Issue Pages 21 pp
Keywords Black-Scholes model; Option pricing; Arbitrage; Barrier options
Abstract In this paper, we want to report an interesting resonance phenomena that appears in option pricing, when the presence of arbitrage is incorporated explicitly into the Black-Scholes model. In Contreras et al. (2010), the authors after analyse empirical financial data, determines that the mispricing between the empirical and the Black-Scholes prices can be described by Heaviside type function (called an arbitrage bubble there). These bubbles are characterised by a finite time span and an amplitude which measures the price deviation from the Black-Scholes model. After that, in Contreras et al. (2010), the Black-Scholes equation is generalised to incorporates explicitly these arbitrage bubbles, which generates an interaction potential that changes the usual Black-Scholes free dynamics completely. However, an interesting phenomena appears when the amplitude of the arbitrage bubble is equal to the volatility parameter of the Black-Scholes model: in that case, the potential becomes infinite, and option pricing decrease abruptly to zero. We analyse this limit behaviour for two situations: a European and a barrier option. Also, we perform an analytic study of the propagator in each case, to understand the cause of the resonance. We think that it resonance phenomena could to help to understand the origin of certain financial crisis in the option pricing area. (C) 2019 Elsevier B.V. All rights reserved.
Address [Contreras, M.; Pena, J. P.] Univ Andres Bello, Dept Ciencias Fis, Sazie 2212, Chile, Email: mauriccio1965@gmail.com;
Corporate Author Thesis
Publisher Elsevier Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000506711900078 Approved
Call Number UAI @ eduardo.moreno @ Serial 1095
Permanent link to this record
 

 
Author (up) Contreras, M.; Hojman, S.A.
Title Option pricing, stochastic volatility, singular dynamics and constrained path integrals Type
Year 2014 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 393 Issue Pages 391-403
Keywords Option pricing; Stochastic volatility; Quantum mechanics; Singular Lagrangian systems; Dirac's method; Constrained Hamiltonian path integrals
Abstract Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993) [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter p which relates the two Brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset. Solutions to the Heston model in the context of option pricing, using a path integral approach, are found in Lemmens et al. (2008) [21] while in Baaquie (2007,1997) [12,13] propagators for different stochastic volatility models are constructed. In all previous cases, the propagator is not defined for extreme cases rho = +/- 1. It is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator. In this paper we study in detail a general class of stochastic volatility models for extreme values rho = +/- 1 and show that in these two cases, the associated classical dynamics corresponds to a system with second class constraints, which must be dealt with using Dirac's method for constrained systems (Dirac, 1958,1967) [22,23] in order to properly obtain the propagator in the form of a Euclidean Hamiltonian path integral (Henneaux and Teitelboim, 1992) [25]. After integrating over momenta, one gets an Euclidean Lagrangian path integral without constraints, which in the case of the Heston model corresponds to a path integral of a repulsive radial harmonic oscillator. In all the cases studied, the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral. (C) 2013 Elsevier B.V. All rights reserved.
Address [Contreras, Mauricio] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000328179200034 Approved
Call Number UAI @ eduardo.moreno @ Serial 335
Permanent link to this record
 

 
Author (up) Contreras, M.; Montalva, R.; Pellicer, R.; Villena, M.
Title Dynamic option pricing with endogenous stochastic arbitrage Type
Year 2010 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 389 Issue 17 Pages 3552-3564
Keywords Black-Scholes model; Arbitrage; Option pricing
Abstract Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started. (C) 2010 Elsevier B.V. All rights reserved.
Address [Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo] Univ Adolfo Ibanez, Fac Sci & Engn, Vina Del Mar, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000280118100023 Approved
Call Number UAI @ eduardo.moreno @ Serial 91
Permanent link to this record
 

 
Author (up) Contreras, M.; Pellicer, R.; Villena, M.
Title Dynamic optimization and its relation to classical and quantum constrained systems Type
Year 2017 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 479 Issue Pages 12-25
Keywords Dynamic optimization; Constrained systems; Dirac's method; Quantum mechanics
Abstract We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop lambda-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Psi (x, t) = e(is(x,t)) in the quantum Schrodinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x, t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem. (C) 2017 Elsevier B.V. All rights reserved.
Address [Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo] Univ Adolfo Ibanez, Fac Engn & Sci, Santiago, Region Metropol, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000400213800002 Approved
Call Number UAI @ eduardo.moreno @ Serial 731
Permanent link to this record
 

 
Author (up) Contreras, M.; Pellicer, R.; Villena, M.; Ruiz, A.
Title A quantum model of option pricing: When Black-Scholes meets Schrodinger and its semi-classical limit Type
Year 2010 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 389 Issue 23 Pages 5447-5459
Keywords Black-Scholes model; Arbitrage; Option pricing; Quantum mechanics; Semi-classical methods
Abstract The Black-Scholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrodinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, short-term volatility, extreme discontinuities, or serial correlations; the classical non-arbitrage assumption of the Black-Scholes model is violated, implying a non-risk-free portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the Black-Scholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new Black-Scholes-Schrodinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrodinger equation in imaginary time for a particle of mass 1/sigma(2) with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the Black-Scholes model represent a particular case. Finally, since the Schrodinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the Black-Scholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrodinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact solution of our general quantum model of option pricing. (C) 2010 Elsevier B.V. All rights reserved.
Address [Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo; Ruiz, Aaron] Adolfo Ibanez Univ, Fac Sci & Engn, Santiago, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000283904000012 Approved
Call Number UAI @ eduardo.moreno @ Serial 116
Permanent link to this record
 

 
Author (up) Contreras, M.; Pena, J.P.
Title The quantum dark side of the optimal control theory Type
Year 2019 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume 515 Issue Pages 450-473
Keywords Optimal control theory; Pontryagin's equations; Hamilton-Jacobi-Bellman equation; Constrained systems; Dirac's method; Quantum mechanics
Abstract In a recent article, a generic optimal control problem was studied from a physicist's point of view (Contreras et al. 2017). Through this optic, the Pontryagin equations are equivalent to the Hamilton equations of a classical constrained system. By quantizing this constrained system, using the right ordering of the operators, the corresponding quantum dynamics given by the Schrodinger equation is equivalent to that given by the Hamilton-Jacobi-Bellman equation of Bellman's theory. The conclusion drawn there were based on certain analogies between the equations of motion of both theories. In this paper, a closer and more detailed examination of the quantization problem is carried out, by considering three possible quantization procedures: right quantization, left quantization, and Feynman's path integral approach. The Bellman theory turns out to be the classical limit h -> 0 of these three different quantum theories. Also, the exact relation of the phase S(x, t) of the wave function Psi(x, t) = e(i/hS(x,t)) of the quantum theory with Bellman's cost function J(+)(x, t) is obtained. In fact, S(x, t) satisfies a 'conjugate' form of the Hamilton-Jacobi-Bellman equation, which implies that the cost functional J(+)(x, t) must necessarily satisfy the usual Hamilton-Jacobi-Bellman equation. Thus, the Bellman theory effectively corresponds to a quantum view of the optimal control problem. (C) 2018 Elsevier B.V. All rights reserved.
Address [Contreras G, Mauricio] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000452941100042 Approved
Call Number UAI @ eduardo.moreno @ Serial 952
Permanent link to this record
 

 
Author (up) Villena, M.J.; Contreras, M.
Title Global And Local Advertising Strategies: A Dynamic Multi-Market Optimal Control Model Type
Year 2019 Publication Journal Of Industrial And Management Optimization Abbreviated Journal J. Ind. Manag. Optim.
Volume 15 Issue 3 Pages 1017-1048
Keywords Advertising strategies; multi-market oligopoly; global advertising; differential games
Abstract Differential games have been widely used to model advertising strategies of companies. Nevertheless, most of these studies have concentrated on the dynamics and market structure of the problem, neglecting their multi-market dimension. Since nowadays competition typically operates on multi-product contexts and usually in geographically separated markets, the optimal advertising strategies must take into consideration the different levels of disaggregation, especially, for example, in retail multi-product and multi-store competition contexts. In this paper, we look into the decision-making process of a multi-market company that has to decide where, when and how much money to invest in advertising. For this purpose, we develop a model that keeps the dynamic and oligopolistic nature of the traditional advertising game introducing the multi-market dimension of today's economies, while differentiating global (i.e. national TV) from local advertising strategies (i.e. a price discount promotion in a particular store). It is important to note, however, that even though this problem is real for most multi-market companies, it has not been addressed in the differential games literature. On the more technical side, we steer away from the traditional aggregated dynamics of advertising games in two aspects. Firstly, we can model different markets at once, obtaining a global instead of a local optimum, and secondly, since we are incorporating a variable that is common to markets, the resulting equations systems for every market are now coupled. In other words, one's decision in one market does not only affect one's competition in that particular market; it also affects one's decisions and one's competitors in all markets.
Address [Villena, Marcelo J.; Contreras, Mauricio] Univ Adolfo Ibanez, Fac Engn & Sci, Av Diagonal Las Torres 2640, Santiago 7941169, Chile, Email: marcelo.villena@uai.cl;
Corporate Author Thesis
Publisher Amer Inst Mathematical Sciences-Aims Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1547-5816 ISBN Medium
Area Expedition Conference
Notes WOS:000466101700002 Approved
Call Number UAI @ eduardo.moreno @ Serial 1021
Permanent link to this record