It is with pleasure that we offer the readers of the International Journal of Computer Mathematics this special issue consisting of some of the most significant contributions to computational and mathematical methods with advanced applications in finance presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2013, held at the Instituto Universitario de Matemática, Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain, September 4–6, 2013, cf. http://jornadas.imm.upv.es/2013/.
Since its founding the International Conference on Mathematical Modelling in Engineering & Human Behaviour has been a truly multi-disciplinary conference, covering all aspects of applied mathematics in a very broad field of areas of science and engineering with its increasing level of complexity. The aim of this conference series is to encourage cross-fertilization between different disciplines and to gain new insights into the emerging research trends in mathematical modelling and engineering methods.
The first paper of this special issue, Kilianová and Trnovská [Citation6], analyses a problem of dynamic stochastic portfolio optimization modelled by a fully non-linear Hamilton–Jacobi–Bellman equation. The authors provide an application to robust portfolio optimization for the German DAX30 Index.
The article The operation of infimal/supremal convolution in mathematical economics, by Bayón et al. [Citation1], considers the infimal convolution operation arising in the analysis of several problems of mathematical economics. Further, the authors present a new application: the analytical solution of the utility maximization problem obtained by applying the supremal convolution operation.
The third article, Optimal allocation-consumption problem for a portfolio with an illiquid asset [Citation2], considers an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. The authors study two different distributions of the liquidation time of the illiquid asset – a classical exponential distribution and a more practically relevant Weibull distribution.
The research by Calvo-Garrido and Vázquez [Citation3] deals with the valuation of fixed-rate mortgages including prepayment and default options, where the underlying stochastic factors are the house price and the interest rate. The pricing model is a free boundary problem associated with a partial differential equation (PDE). Appropriate numerical methods based on a Lagrange–Galerkin discretization of the PDE, an augmented Lagrangian active set method and a Newton iteration scheme are proposed.
In their work, On splitting-based numerical methods for nonlinear models of European options, Koleva and Vulkov [Citation7], study a large class of non-linear models of European options as parabolic equations with quasi-linear diffusion and fully non-linear hyperbolic part. The authors apply the operator splitting method to couple known difference schemes for non-linear hyperbolic equations with other ones for quasi-linear parabolic equations.
In Using the building energy rating software for mathematically modelling operation costs in a simulated home [Citation8], the authors consider two software tools Lider and Calener to simulate energy performance in new semi-detached houses in Spain to obtain mathematical models that explain the behaviour of global costs of buildings based on energy ratings and climatic zones.
The work, On the understanding of profiles by means of post-processing techniques: An application to financial assets [Citation4], considers the application of knowledge discovery in databases to support analysis and decision-making regarding complex financial phenomena. Here, clustering is used to mine financial patterns from Venezuelan Stock Exchange assets (Bolsa de Valores de Caracas), and two major indexes related to that market: Dow Jones (USA) and BOVESPA (Brazil).
Gyulov and Valkov [Citation5] apply the monotonic penalty method to reformulate the option pricing linear complementarity problem, transformed on finite interval. A fitted finite volume method is proposed that supports their theoretical findings.
Finally, we thank all the authors and referees for their excellent contributions to this special volume. We also express our gratitude to Helen Gray and Louise Evans from the Taylor & Francis Group for their continuous support in preparing this special issue.
Disclosure statement
No potential conflict of interest was reported by the authors.
References
- L. Bayón, P.J. García-Nieto, R. García-Rubio, J.M. Grau, M.M. Ruiz, and P.M. Suárez, The operation of infimal/supremal convolution in mathematical economics, Int. J. Comput. Math. (2015).
- L.A. Bordag, I.P. Yamshchikov, and D. Zhelezov, Optimal allocation-consumption problem for a portfolio with an illiquid asset, Int. J. Comput. Math. (2015).
- M.C. Calvo-Garrido and C. Vázquez, A new numerical method for pricing fixed-rate mortgages with prepayment and default options, Int. J. Comput. Math. (2015).
- K. Gibert, D. Conti, On the understanding of profiles by means of post-processing techniques: An application to financial assets, Int. J. Comput. Math. (2015).
- T.B. Gyulov and R.L. Valkov, American option pricing problem transformed on finite interval, Int. J. Comput. Math. (2015).
- S. Kilianová and M. Trnovská, Robust portfolio optimization via solution to the Hamilton-Jacobi-Bellman equation, Int. J. Comput. Math. (2015).
- M.N. Koleva and L.G. Vulkov, On splitting-based numerical methods for nonlinear models of European options, Int. J. Comput. Math. (2015).
- M.J. Ruá and N. Guadalajara, Using the building energy rating software for mathematically modelling operation costs in a simulated home, Int. J. Comput. Math. (2015).