43 47 7 2 ; S ; [EN] This paper critically analyses the implications the digitalisation process has on individuals and organization `s behaviour. The digital era has positive aspects such as the access to information on real time from almost any geographical place combined with the shorten the length of time of processes. In addition, new economic trends and paradigms emerge in the digital era. However, we cannot deny the existence of negative or at least unexpected aspects of the digitalization. This work highlights some of the most alarming aspects of digitization that require the attention and implementation of measures by public authorities to prevent from the collateral damages the digitalisation can produce on citizenship well-being. De La Poza, E.; Jódar Sánchez, LA. (2019). Modelling Human Behaviour in the Digital Era: Economic and Social Impacts. Economics. 7(2):43-47. https://doi.org/10.2478/eoik-2019-0015
[EN] This paper is aimed to extend, the non-autonomous case, the results recently given in the paper [1] for solving autonomous linear and quadratic random matrix differential equations. With this goal, important deterministic results like the Abel-Liouville-Jacobi's formula, are extended to the random scenario using the so-called $\mathrm{L}_{p}$-random matrix calculus. In a first step, random time-dependent matrix linear differential equations are studied and, in a second step, random non-autonomous Riccati matrix differential equations are solved using the hamiltonian approach based on dealing with the extended underlying linear system. Illustrative numerical examples are also included. [1] M.-C. Casabán, J.-C. Cortés, L. Jódar, Solving linear and quadratic random matrix differential equations: A mean square approach, Applied Mathematical Modelling 40 (2016) 9362-9377. ; This work has been partially supported by the Spanish Ministerio de Economia y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance). ; Casabán, M.; Cortés, J.; Jódar Sánchez, LA. (2018). Solving linear and quadratic random matrix differential equations using: A mean square approach. The non-autonomous case. Journal of Computational and Applied Mathematics. 330:937-954. https://doi.org/10.1016/j.cam.2016.11.049 ; S ; 937 ; 954 ; 330
937 954 330 ; S ; [EN] This paper is aimed to extend, the non-autonomous case, the results recently given in the paper [1] for solving autonomous linear and quadratic random matrix differential equations. With this goal, important deterministic results like the Abel-Liouville-Jacobi's formula, are extended to the random scenario using the so-called $\mathrm{L}_{p}$-random matrix calculus. In a first step, random time-dependent matrix linear differential equations are studied and, in a second step, random non-autonomous Riccati matrix differential equations are solved using the hamiltonian approach based on dealing with the extended underlying linear system. Illustrative numerical examples are also included. [1] M.-C. Casabán, J.-C. Cortés, L. Jódar, Solving linear and quadratic random matrix differential equations: A mean square approach, Applied Mathematical Modelling 40 (2016) 9362-9377. This work has been partially supported by the Spanish Ministerio de Economia y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance). Casabán, M.; Cortés, J.; Jódar Sánchez, LA. (2018). Solving linear and quadratic random matrix differential equations using: A mean square approach. The non-autonomous case. Journal of Computational and Applied Mathematics. 330:937-954. https://doi.org/10.1016/j.cam.2016.11.049
[EN] This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. Using the so-called Lp-random calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized power series solution is constructed. As a result of this convergence, the sequences of the mean and standard deviation obtained from the truncated power series solution are convergent as well. The results obtained in the random framework extend their deterministic counterpart. The theory is illustrated in two examples in which several distributions on the random inputs are assumed. Finally, we show through examples that the proposed method is computationally faster than Monte Carlo method. ; This work has been partially supported by the Spanish Ministerio de Economía y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement No. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and Mexican Conacyt. ; Cortés, J.; Jódar Sánchez, LA.; Villafuerte, L. (2017). Mean square solution of Bessel differential equation with uncertainties. Journal of Computational and Applied Mathematics. 309:383-395. https://doi.org/10.1016/j.cam.2016.01.034 ; S ; 383 ; 395 ; 309
[EN] This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach. ; This work has been partially supported by the European Union in the FP7- PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Econom´ıa y Competitividad Spanish Grant MTM2013-41765-P. ; Company Rossi, R.; Egorova, V.; Jódar Sánchez, LA. (2016). An efficient method for solving spread option pricing problem: numerical analysis and computing. Abstract and Applied Analysis. 2016:1-11. https://doi.org/10.1155/2016/1549492 ; S ; 1 ; 11 ; 2016 ; Carmona, R., & Durrleman, V. (2003). Pricing and Hedging Spread Options. SIAM Review, 45(4), 627-685. doi:10.1137/s0036144503424798 ; Boyle, P. P. (1977). Options: A Monte Carlo approach. Journal of Financial Economics, 4(3), 323-338. doi:10.1016/0304-405x(77)90005-8 ; Joy, C., Boyle, P. P., & Tan, K. S. (1996). Quasi-Monte Carlo Methods in Numerical Finance. Management Science, 42(6), 926-938. doi:10.1287/mnsc.42.6.926 ; Kao, W.-H., Lyuu, Y.-D., & Wen, K.-W. (2014). The hexanomial lattice for pricing multi-asset options. Applied Mathematics and Computation, 233, 463-479. doi:10.1016/j.amc.2014.01.173 ; Pearson, N. D. (1995). An Efficient Approach for Pricing Spread Options. The Journal of Derivatives, 3(1), 76-91. doi:10.3905/jod.1995.407928 ; Chiarella, C., & Ziveyi, J. (2013). Pricing American options written on two underlying assets. Quantitative Finance, 14(3), 409-426. doi:10.1080/14697688.2013.810811 ; Boyle, P. P. (1988). A Lattice ...
[EN] A system of coupled free boundary problems describing American put option pricing under regime switching is considered. In order to build numerical solution firstly a front-fixing transformation is applied. Transformed problem is posed on multidimensional fixed domain and is solved by explicit finite difference method. The numerical scheme is conditionally stable and is consistent with the first order in time and second order in space. The proposed approach allows the computation not only of the option price but also of the optimal stopping boundary. Numerical examples demonstrate efficiency and accuracy of the proposed method. The results are compared with other known approaches to show its competitiveness. ; This work has been partially supported by the European Union in the FP7- PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P. ; Egorova, V.; Company Rossi, R.; Jódar Sánchez, LA. (2016). A New Efficient Numerical Method for Solving American Option under Regime Switching Model. Computers and Mathematics with Applications. 71:224-237. https://doi.org/10.1016/j.camwa.2015.11.019 ; S ; 224 ; 237 ; 71
[EN] A new front-fixing transformation is applied to the Black Scholes equation for the American call option pricing problem. The transformed non-linear problem involves homogeneous boundary conditions independent of the free boundary. The numerical solution by an explicit finite-difference method is positive and monotone. Stability and consistency of the scheme are studied. The explicit proposed method is compared with other competitive implicit ones from the points of view accuracy and computational cost. ; This paper has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance). ; Company Rossi, R.; Egorova, V.; Jódar Sánchez, LA. (2016). Constructing positive reliable numerical solution for American call options: a new front-fixing approach. Journal of Computational and Applied Mathematics. 291:422-431. https://doi.org/10.1016/j.cam.2014.09.013 ; S ; 422 ; 431 ; 291
This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach. ; This work has been partially supported by the European Union in the FP7- PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economía y Competitividad Spanish Grant MTM2013-41765-P.
[EN] This paper presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. Numerical analysis of the method is provided. The method preserves positivity and monotonicity of the numerical solution. Consistency and stability properties of the scheme are studied. Explicit calculations avoid iterative algorithms for solving nonlinear systems. Theoretical results are confirmed by numerical experiments. Comparison with other approaches shows that the proposed method is accurate and competitive. ; This paper has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance). ; Company Rossi, R.; Egorova, V.; Jódar Sánchez, LA. (2014). Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing. Abstract and Applied Analysis. 2014:1-9. https://doi.org/10.1155/2014/146745 ; S ; 1 ; 9 ; 2014 ; Feng, L., Linetsky, V., Luis Morales, J., & Nocedal, J. (2011). On the solution of complementarity problems arising in American options pricing. Optimization Methods and Software, 26(4-5), 813-825. doi:10.1080/10556788.2010.514341 ; Van Moerbeke, P. (1976). On optimal stopping and free boundary problems. Archive for Rational Mechanics and Analysis, 60(2), 101-148. doi:10.1007/bf00250676 ; GESKE, R., & JOHNSON, H. E. (1984). The American Put Option Valued Analytically. The Journal of Finance, 39(5), 1511-1524. doi:10.1111/j.1540-6261.1984.tb04921.x ; BARONE-ADESI, G., & WHALEY, R. E. (1987). Efficient Analytic Approximation of American Option Values. The Journal of Finance, 42(2), 301-320. doi:10.1111/j.1540-6261.1987.tb02569.x ; Ju, N. (1998). Pricing by American Option by Approximating its Early Exercise Boundary as a Multipiece Exponential Function. Review of Financial Studies, 11(3), ...
[EN] This paper provides a numerical analysis for European options under partial integro-differential Bates model. An explicit finite difference scheme has been used for the differential part, while the integral part has been approximated using the four-points open type formula. The stability and consistency have been studied. Moreover, conditions guaranteing positivity of the solutions are provided. Illustrative numerical examples are included. ; This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P. ; Fakharany, M.; Company Rossi, R.; Jódar Sánchez, LA. (2014). Positive finite difference schemes for a partial integro-differential option pricing model. Applied Mathematics and Computation. 249:320-332. https://doi.org/10.1016/j.amc.2014.10.064 ; S ; 320 ; 332 ; 249
[EN] In recent decades, pathological consumption has become a growing behavioral misbehavior. Impulsive consumption is governed by two internal behavioral mechanisms that respond fundamentally to the hedonism or Pascal effect and to the emulation or Veblen effect. Today's development of technology acts as a catalyst of consumption by increasing access and availability to products, as well as the advertisement impact. This paper presents a compartmental discrete matrix mathematical model that allows short-term estimates of ordinary, impulsive, and pathological buyers in Spain in three different economic scenarios. The results show that impulsive and pathological buyers will increase in all the economic scenarios. Notable differences in the number of ordinary buyers are found for the group aged over 65 years. ; Ministerio de Ciencia, Innovacion y Universidades, Grant/Award Numbers: Spanish MTM2017-89664-P ; Merello, P.; De La Poza, E.; Jódar Sánchez, LA. (2020). Explaining shopping behavior in a market economy country: A short-term mathematical model applied to the case of Spain. Mathematical Methods in the Applied Sciences. 43(14):8089-8104. https://doi.org/10.1002/mma.6072 ; S ; 8089 ; 8104 ; 43 ; 14 ; Reith, G. (2004). Consumption and its discontents: addiction, identity and the problems of freedom. The British Journal of Sociology, 55(2), 283-300. doi:10.1111/j.1468-4446.2004.00019.x ; Althofer J Musgrove B. "A Ghost in Daylight" Drugs and the Horror of Modernity. Basingstoke UK: Palgrave Communications; 2018 4 112. ; Hunter, K. M. B. (2016). Shopaholic stories: Tales of therapeutic addiction, governance, and political economy. Journal of Consumer Culture, 18(4), 497-519. doi:10.1177/1469540516684186 ; Tsai, W. S., Yang, Q., & Liu, Y. (2013). Young Chinese Consumers' Snob and Bandwagon Luxury Consumption Preferences. Journal of International Consumer Marketing, 25(5), 290-304. doi:10.1080/08961530.2013.827081 ; Leibenstein, H. (1950). Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand. ...
De La Poza, E.; Jódar Sánchez, LA.; Merello, P. (2019). Modeling the political corruption in Spain. R. Company, J. C. Cortés, L. Jódar and E. López-Navarro. 70-74. http://hdl.handle.net/10251/180556 ; S ; 70 ; 74
[EN] In this paper, numerical analysis of finite difference schemes for partial integro-differential models related to European and American option pricing problems under a wide class of Lévy models is studied. Apart from computational and accuracy issues, qualitative properties such as positivity are treated. Consistency of the proposed numerical scheme and stability in the von Neumann sense are included. Gauss Laguerre quadrature formula is used for the discretization of the integral part. Numerical examples illustrating the potential advantages of the presented results are included. ; This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P. ; El-Fakharany, M.; Company Rossi, R.; Jódar Sánchez, LA. (2016). Solving partial integro-differential option pricing problems for a wide class of infinite activity Lévy processes. Journal of Computational and Applied Mathematics. 296:739-752. https://doi.org/10.1016/j.cam.2015.10.027 ; S ; 739 ; 752 ; 296
