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Dr. Marcelo Villena
Universidad Adolfo Ibáñez, Diagonal Las Torres 2640 Peñalolén, Santiago de Chile, Chile

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0 Environmental Economics
0 Productivity
0 circular economy
0 Operation Research
0 Supply-chain Management

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Journal article
Published: 07 November 2020 in Journal of Computational and Applied Mathematics
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The CEV model allows volatility to change with the underlying price, capturing a basic empirical regularity very relevant for option pricing, such as the volatility smile. Nevertheless, the standard CEV solution, using the non-central chi-square approach, still presents high computational times. In this paper, the CEV option pricing formula is computed using the semiclassical approximation of Feynman’s path integral. Our simulations show that the method is quite efficient and accurate compared to the standard CEV solution considering the pricing of European call options.

ACS Style

Axel A. Araneda; Marcelo J. Villena. Computing the CEV option pricing formula using the semiclassical approximation of path integral. Journal of Computational and Applied Mathematics 2020, 388, 113244 .

AMA Style

Axel A. Araneda, Marcelo J. Villena. Computing the CEV option pricing formula using the semiclassical approximation of path integral. Journal of Computational and Applied Mathematics. 2020; 388 ():113244.

Chicago/Turabian Style

Axel A. Araneda; Marcelo J. Villena. 2020. "Computing the CEV option pricing formula using the semiclassical approximation of path integral." Journal of Computational and Applied Mathematics 388, no. : 113244.

Journal article
Published: 27 May 2020 in Computers & Mathematics with Applications
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In this paper, we analyze the effects of vaccination from a spatial perspective. We propose a spatial deterministic SIRS–V model, which considers a non-linear system of partial differential equations with explicit attrition and diffusion terms for the vaccination process. The model allows us to simulate numerically the spatial and temporal dynamics of an epidemic, considering different spatial strategies for the vaccination policy. In particular, in our first example we analyze the classical SIRS–V evolution with the addition of movements due to diffusion, while in the second one we focus on modeling one ring vaccination policy. We expect this model can improve spatial predictions of SIR vaccination models by taking into account the spatial dimension of the problem.

ACS Style

Eduardo González; Marcelo J. Villena. On the spatial dynamics of vaccination: A spatial SIRS–V model. Computers & Mathematics with Applications 2020, 80, 733 -743.

AMA Style

Eduardo González, Marcelo J. Villena. On the spatial dynamics of vaccination: A spatial SIRS–V model. Computers & Mathematics with Applications. 2020; 80 (5):733-743.

Chicago/Turabian Style

Eduardo González; Marcelo J. Villena. 2020. "On the spatial dynamics of vaccination: A spatial SIRS–V model." Computers & Mathematics with Applications 80, no. 5: 733-743.

Journal article
Published: 06 November 2019 in Sustainability
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Urban residual flows contain significant amounts of valuable nutrients, which, if recovered, could serve as input for the own city needs or those of its immediate surroundings. In this study, the possibilities for decentralized recovery of nutrient rich residual flows in Santiago, Chile, are studied by means of a case study considering technical and socio-economic criteria. In particular, we calculate circularity indicators for organic matter (OM), nitrogen (N), and phosphorus (P) and cost–benefits of household and community on-site technological alternatives. Kitchen waste (KW) and garden residues (GR) as well as urine were considered as system inputs whereas urban agriculture, municipality green, or peri-urban agriculture were the considered destinations for nutrients recovered. The technologies studied were anaerobic digestion, vermicomposting, and composting, while urine storage and struvite precipitation were considered for nutrient recovery from urine. Material flow analysis was used to visualize the inputs and outputs of the baseline situation (the traditional urban waste management system), and of the different household and municipality resource recovery scenarios (the decentralized valorization systems). Our findings show that decentralized valorization of KW and GR are a clear win–win policy, since they can not only produce important environmental benefits for the city in the long run, but also important cost savings considering the landfill fees and residues transportation of the current centralized waste management system.

ACS Style

Jeltsje De Kraker; Katarzyna Kujawa-Roeleveld; Marcelo J. Villena; Claudia Pabón-Pereira. Decentralized Valorization of Residual Flows as an Alternative to the Traditional Urban Waste Management System: The Case of Peñalolén in Santiago de Chile. Sustainability 2019, 11, 6206 .

AMA Style

Jeltsje De Kraker, Katarzyna Kujawa-Roeleveld, Marcelo J. Villena, Claudia Pabón-Pereira. Decentralized Valorization of Residual Flows as an Alternative to the Traditional Urban Waste Management System: The Case of Peñalolén in Santiago de Chile. Sustainability. 2019; 11 (22):6206.

Chicago/Turabian Style

Jeltsje De Kraker; Katarzyna Kujawa-Roeleveld; Marcelo J. Villena; Claudia Pabón-Pereira. 2019. "Decentralized Valorization of Residual Flows as an Alternative to the Traditional Urban Waste Management System: The Case of Peñalolén in Santiago de Chile." Sustainability 11, no. 22: 6206.

Journal article
Published: 19 October 2019 in Physica A: Statistical Mechanics and its Applications
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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.

ACS Style

M. Contreras; J. Echeverría; J.P. Peña; M. Villena. Resonance phenomena in option pricing with arbitrage. Physica A: Statistical Mechanics and its Applications 2019, 540, 123238 .

AMA Style

M. Contreras, J. Echeverría, J.P. Peña, M. Villena. Resonance phenomena in option pricing with arbitrage. Physica A: Statistical Mechanics and its Applications. 2019; 540 ():123238.

Chicago/Turabian Style

M. Contreras; J. Echeverría; J.P. Peña; M. Villena. 2019. "Resonance phenomena in option pricing with arbitrage." Physica A: Statistical Mechanics and its Applications 540, no. : 123238.

Journal article
Published: 01 November 2018 in Resources Policy
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How resource depletion affects productivity is a crucial question for several industries. In fact, several natural resource-exporting countries have seen their productivity levels affected by resource depletion. Nevertheless, usually, it is not clear what the real productivity growth is, without discarding the effects of resource depletion in the production structure. The main aim of the paper is to empirically answer a relevant issue regarding the Chilean copper mining industry, which is, the slowdown of its productivity in the last decade, considering in the analysis the role of resource depletion. In particular, we consider resource depletion to be an exogenous and unpaid force that opposes technological change and hence increases costs through time, capturing in this way some stylized facts of, for example, the mining and fishing industries. The decomposition framework was applied to the Chilean copper mining industry, one of the most important in the world, using data from the period of 1985–2015. The econometric results were robust and pointed to the fact that the productivity fell sharply during the period; however, it did not fall as much as the traditional estimation methods pointed out. Our model showed that as much as 15% of this decline was due to the increase of the resource depletion variable (copper ore grade).

ACS Style

Marcelo Villena; Fernando Greve. On resource depletion and productivity: The case of the Chilean copper industry. Resources Policy 2018, 59, 553 -562.

AMA Style

Marcelo Villena, Fernando Greve. On resource depletion and productivity: The case of the Chilean copper industry. Resources Policy. 2018; 59 ():553-562.

Chicago/Turabian Style

Marcelo Villena; Fernando Greve. 2018. "On resource depletion and productivity: The case of the Chilean copper industry." Resources Policy 59, no. : 553-562.

Journal article
Published: 01 January 2017 in Journal of Industrial & Management Optimization
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ACS Style

Marcelo J. Villena; Mauricio Contreras. Global and local advertising strategies: A dynamic multi-market optimal control model. Journal of Industrial & Management Optimization 2017, 13, 1 -11.

AMA Style

Marcelo J. Villena, Mauricio Contreras. Global and local advertising strategies: A dynamic multi-market optimal control model. Journal of Industrial & Management Optimization. 2017; 13 (5):1-11.

Chicago/Turabian Style

Marcelo J. Villena; Mauricio Contreras. 2017. "Global and local advertising strategies: A dynamic multi-market optimal control model." Journal of Industrial & Management Optimization 13, no. 5: 1-11.

Journal article
Published: 01 October 2016 in European Journal of Operational Research
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One key assumption of Markowitz’s model is that all traders act as price takers. In this paper, we extend this mean-variance approach in a setting where large investors can move prices. Instead of having an individual optimization problem, we find the investors’ Nash equilibrium and redefine the efficient frontier in this new framework. We also develop a simplified application of the general model, with two assets and two investors to shed light on the potential strategic behavior of large and atomic investors. Our findings validate the claim that large investors enhance their portfolio performance in relation to perfect market conditions. Besides, we show under which conditions atomic investors can benefit in relation to the standard setting, even if they have not total influence on their eventual performance. The ’two investors-two assets’ setting allows us to quantify performance and do sensitivity analysis regarding investors’ market power, risk tolerance and price elasticity of demand. Finally, for a group of well known ETFs, we empirically show how price variations change depending on the volume traded. We also explain how to set up and use our model with real market data.

ACS Style

Marcelo J. Villena; Lorenzo Reus. On the strategic behavior of large investors: A mean-variance portfolio approach. European Journal of Operational Research 2016, 254, 679 -688.

AMA Style

Marcelo J. Villena, Lorenzo Reus. On the strategic behavior of large investors: A mean-variance portfolio approach. European Journal of Operational Research. 2016; 254 (2):679-688.

Chicago/Turabian Style

Marcelo J. Villena; Lorenzo Reus. 2016. "On the strategic behavior of large investors: A mean-variance portfolio approach." European Journal of Operational Research 254, no. 2: 679-688.

Preprint
Published: 05 July 2016
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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 Schr\"odinger 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.

ACS Style

Mauricio Contreras; Rely Pellicer; Marcelo Villena. Dynamic optimization and its relation to classical and quantum constrained systems. 2016, 1 .

AMA Style

Mauricio Contreras, Rely Pellicer, Marcelo Villena. Dynamic optimization and its relation to classical and quantum constrained systems. . 2016; ():1.

Chicago/Turabian Style

Mauricio Contreras; Rely Pellicer; Marcelo Villena. 2016. "Dynamic optimization and its relation to classical and quantum constrained systems." , no. : 1.

Journal article
Published: 01 January 2016 in Journal of Mathematical Finance
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An non-equilibrium Black-Scholes model, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f (t)W(t), accounting for market imperfections and prices non-alignment, is developed. The white noise amplitude f (t), called arbitrage bubble, generates a time dependent potential U(t) which changes the usual equilibrium dynamics of the traditional Black-Scholes model. The purpose of this article is to tackle the inverse problem, that is, is it possible to extract the time dependent potential U(t) and its associated bubble shape f (t), from the real empirical financial data? In order to give an answer to this question, the interacting Black-Scholes equation must be interpreted as a quantum Schrodinger equation with Hamiltonian operator H=H0+ U(t), where H0 is the equilibrium Black-Scholes Hamiltonian and U(t) is the interaction term. By using semi-classical considerations and the knowledge about the mispricing of the financial data, one can determinate an approximate functional form of the potential term U(t) and its associated bubble f (t), In all the studied cases, the non-equilibrium model performs a better estimation of the real data than the usual equilibrium model. It is expected that this new and simple methodology could help to improve option pricing estimations.

ACS Style

Mauricio Contreras; Rely Pellicer; Daniel Santiagos; Marcelo Villena. Calibration and Simulation of Arbitrage Effects in a Non-Equilibrium Quantum Black-Scholes Model by Using Semi-Classical Methods. Journal of Mathematical Finance 2016, 06, 541 -561.

AMA Style

Mauricio Contreras, Rely Pellicer, Daniel Santiagos, Marcelo Villena. Calibration and Simulation of Arbitrage Effects in a Non-Equilibrium Quantum Black-Scholes Model by Using Semi-Classical Methods. Journal of Mathematical Finance. 2016; 06 (04):541-561.

Chicago/Turabian Style

Mauricio Contreras; Rely Pellicer; Daniel Santiagos; Marcelo Villena. 2016. "Calibration and Simulation of Arbitrage Effects in a Non-Equilibrium Quantum Black-Scholes Model by Using Semi-Classical Methods." Journal of Mathematical Finance 06, no. 04: 541-561.

Journal article
Published: 01 January 2016 in Journal of Mathematical Finance
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In this paper, the multi-asset Black-Scholes model is studied in terms of the importance that the correlation parameter space (equivalent to an N dimensional hypercube) has in the solution of the pricing problem. It is shown that inside of this hypercube there is a surface, called the Kummer surface ∑k, where the determinant of the correlation matrix ρ is zero, so the usual formula for the propagator of the N asset Black-Scholes equation is no longer valid. Worse than that, in some regions outside this surface, the determinant of ρ becomes negative, so the usual propagator becomes complex and divergent. Thus the option pricing model is not well defined for these regions outside ∑k. On the Kummer surface instead, the rank of the ρ matrix is a variable number. By using the Wei-Norman theorem, the propagator over the variable rank surface ∑k for the general N asset case is computed. Finally, the three assets case and its implied geometry along the Kummer surface is also studied in detail.

ACS Style

Mauricio Contreras; Alejandro Llanquihuén; Marcelo Villena. On the Solution of the Multi-Asset Black-Scholes Model: Correlations, Eigenvalues and Geometry. Journal of Mathematical Finance 2016, 06, 562 -579.

AMA Style

Mauricio Contreras, Alejandro Llanquihuén, Marcelo Villena. On the Solution of the Multi-Asset Black-Scholes Model: Correlations, Eigenvalues and Geometry. Journal of Mathematical Finance. 2016; 06 (04):562-579.

Chicago/Turabian Style

Mauricio Contreras; Alejandro Llanquihuén; Marcelo Villena. 2016. "On the Solution of the Multi-Asset Black-Scholes Model: Correlations, Eigenvalues and Geometry." Journal of Mathematical Finance 06, no. 04: 562-579.

Preprint
Published: 14 October 2015
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In this article, the long-term behavior of the stock market index of the New York Stock Exchange is studied, for the period 1950 to 2013. Specifically, the CRSP Value-Weighted and CRSP Equal-Weighted index are analyzed in terms of market efficiency, using the standard ratio variance test, considering over 1600 one week rolling windows. For the equally weighted index, the null hypothesis of random walk is rejected in the whole period, while for the weighted market value index, the null hypothesis start to be accepted from the 1990s. In order to explain this difference, we raised the hypothesis that this behavior can be explained by the joint action of portfolios and non-synchronous trading effects. To check the feasibility of the above assumption, we performed a simulation of both effects, on two- and six-asset portfolios. The results showed that it is possible to explain the empirical difference between the two index, almost entirely by the joint effects of portfolio and non-synchronous trading.

ACS Style

Roberto Ortiz; Mauricio Contreras; Marcelo Villena. On the Efficient Market Hypothesis of Stock Market Indexes: The Role of Non-synchronous Trading and Portfolio Effects. 2015, 1 .

AMA Style

Roberto Ortiz, Mauricio Contreras, Marcelo Villena. On the Efficient Market Hypothesis of Stock Market Indexes: The Role of Non-synchronous Trading and Portfolio Effects. . 2015; ():1.

Chicago/Turabian Style

Roberto Ortiz; Mauricio Contreras; Marcelo Villena. 2015. "On the Efficient Market Hypothesis of Stock Market Indexes: The Role of Non-synchronous Trading and Portfolio Effects." , no. : 1.

Journal article
Published: 16 April 2014 in Water Policy
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This research focuses on the determination of the factors that led to the failure of water management in the Copiapó Basin in Chile. Interestingly, the existence of full private ownership and free tradability of water rights has not prevented the overexploitation of groundwater resources. In the paper, firstly, water regulation and the role of the regulator in Chile are briefly discussed. Secondly, the evolution of water resources in the Copiapó region is characterized and analyzed, and the granting of water use rights in the basin in the last 30 years is concisely described. Thirdly, we examine and analyze prices and quantities traded in the water market of the Copiapó region. We will argue that this crisis is a consequence first of failure in regulatory implementation and second of an extremely rigid regulatory framework that leaves limited room for adjustment to changing conditions, especially regarding the emergence of new information concerning water availability. We believe this investigation is not only relevant for this case in particular, but also for other regions and countries where water markets are in place.

ACS Style

Eduardo Bitran; Pedro Rivera; Marcelo J. Villena. Water management problems in the Copiapó Basin, Chile: markets, severe scarcity and the regulator. Water Policy 2014, 16, 844 -863.

AMA Style

Eduardo Bitran, Pedro Rivera, Marcelo J. Villena. Water management problems in the Copiapó Basin, Chile: markets, severe scarcity and the regulator. Water Policy. 2014; 16 (5):844-863.

Chicago/Turabian Style

Eduardo Bitran; Pedro Rivera; Marcelo J. Villena. 2014. "Water management problems in the Copiapó Basin, Chile: markets, severe scarcity and the regulator." Water Policy 16, no. 5: 844-863.