Related papers: Numerical valuation of American basket options via…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial…
In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under the framework of the difference of convex functions (DC) approach, a…
The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
We propose to solve polynomial hyperbolic partial differential equations (PDEs) with convex optimization. This approach is based on a very weak notion of solution of the nonlinear equation, namely the measure-valued (mv) solution,…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
We consider an important class of derivative contracts written on multiple assets (so-called spread options) which are traded on a wide range of financial markets. The present paper introduces a new approximation method of density functions…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…
The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor…
In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We…