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Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $\alpha \in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we…
Recently, the numerical solution of multi-frequency, highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. When the problem derives from the space semi-…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the…
In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
We present a primal--dual memory efficient algorithm for solving a relaxed version of the general transportation problem. Our approach approximates the original cost function with a differentiable one that is solved as a sequence of…
We show how inter-asset dependence information derived from market prices of options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the traded option, we either extract correlation…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the…
Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE based option pricing models can be described by solutions to the generalized Black-Scholes parabolic…
Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling of natural phenomena and man made complex systems. In particular, parabolic PDEs are a fundamental tool to determine fair prices of financial…
In recent years, quantitative investment methods combined with artificial intelligence have attracted more and more attention from investors and researchers. Existing related methods based on the supervised learning are not very suitable…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
In this paper, the TF system of two-coupled Black-Scholes equations for pricing the convertible bonds is solved numerically by using the P1 and P2 finite elements with the inequality constraints approximated by the penalty method. The…