Novel methods in computational finance

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 [6], 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. [1], 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 [2], considers an optimization problem for a portfolio with an illiquid, a risky and a riskfree 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 [3] 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 [7], 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

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