Related papers: Sharp Estimates for Geman-Yor Processes and applic…

In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only the absence of arbitrage opportunities. We formulate this as…

We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…

A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the…

We introduce a modification to the patchy method of Navasca and Krener for solving the stationary Hamilton Jacobi Bellman equation. The numerical solution that we generate is a set of polynomials that approximate the optimal cost and…

We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…

Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation…

We obtain two-sided bounds for the density of stochastic processes satisfying a weak H\"ormander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various…

We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…

We present a new method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on Haar series and extreme values of the point process. We give…

In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…

We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that…

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…

In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…

We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…

In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…

We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new…

We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…

We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…