Related papers: Explicit RKF-Compact Scheme for Pricing Regime Swi…
We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…
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…
In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage…
Bernoulli free boundary problem is numerically solved via shape optimization that minimizes a cost functional subject to state problems constraints. In \cite{1}, an energy-gap cost functional was formulated based on two auxiliary state…
Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order…
We study the binomial, trinomial, and Black-Scholes-Merton models of option pricing. We present fast parallel discrete-time finite-difference algorithms for American call option pricing under the binomial and trinomial models and American…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
Despite significant advancements in machine learning for derivative pricing, the efficient and accurate valuation of American options remains a persistent challenge due to complex exercise boundaries, near-expiry behavior, and intricate…
Many real-world settings involve costs for performing actions; transaction costs in financial systems and fuel costs being common examples. In these settings, performing actions at each time step quickly accumulates costs leading to vastly…
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options,…
The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no…
The problem of optimal switching between nonlinear autonomous subsystems is investigated in this study where the objective is not only bringing the states to close to the desired point, but also adjusting the switching pattern, in the sense…
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…
We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to $k$ trades, where each trade must involve the…
This paper concerns the numerical solution of the two-dimensional time-dependent partial integro-differential equation (PIDE) that holds for the values of European-style options under the two-asset Kou jump-diffusion model. A main feature…
We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…