John Schoenmakers
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View article: Primal and dual optimal stopping with signatures
Primal and dual optimal stopping with signatures Open
We propose two signature-based methods to solve an optimal stopping problem – that is, to price American options – in non-Markovian frameworks. Both methods rely on a global approximation result for $L^{p}$ -functionals on rough-path s…
View article: Weighted mesh algorithms for general Markov decision processes: Convergence and tractability
Weighted mesh algorithms for general Markov decision processes: Convergence and tractability Open
We introduce a mesh-type approach for tackling discrete-time, finite-horizon Markov Decision Processes (MDPs) characterized by state and action spaces that are general, encompassing both finite and infinite (yet suitably regular) subsets o…
View article: Primal and dual optimal stopping with signatures
Primal and dual optimal stopping with signatures Open
We propose two signature-based methods to solve the optimal stopping problem - that is, to price American options - in non-Markovian frameworks. Both methods rely on a global approximation result for $L^p-$functionals on rough path-spaces,…
View article: Optimal Stopping with Randomly Arriving Opportunities to Stop
Optimal Stopping with Randomly Arriving Opportunities to Stop Open
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on rand…
View article: From optimal martingales to randomized dual optimal stopping
From optimal martingales to randomized dual optimal stopping Open
In this article we study and classify optimal martingales in the dual formulation of optimal stopping problems. In this respect we distinguish between weakly optimal and surely optimal martingales. It is shown that the family of weakly opt…
View article: Optimal stopping with signatures
Optimal stopping with signatures Open
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by lin…
View article: Primal-dual regression approach for Markov decision processes with general state and action space
Primal-dual regression approach for Markov decision processes with general state and action space Open
We develop a regression based primal-dual martingale approach for solving finite time horizon MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of t…
View article: A Reproducing Kernel Hilbert Space approach to singular local stochastic volatility McKean-Vlasov models
A Reproducing Kernel Hilbert Space approach to singular local stochastic volatility McKean-Vlasov models Open
Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean-Vlasov equation $$ d X_t= σ(t,X_t) X_t \frac{\sqrt v_t}{\sqrt {E[v_t|X_t]}}dW_t, $$ where $W$ is a…
View article: Randomized Optimal Stopping Algorithms and Their Convergence Analysis
Randomized Optimal Stopping Algorithms and Their Convergence Analysis Open
In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the corresp…
View article: Reinforced optimal control
Reinforced optimal control Open
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards b…
View article: Dynamic programming for optimal stopping via pseudo-regression
Dynamic programming for optimal stopping via pseudo-regression Open
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding L2 inner products instead of the least-squar…
View article: Robust Multiple Stopping -- A Pathwise Duality Approach
Robust Multiple Stopping -- A Pathwise Duality Approach Open
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model uncer…
View article: Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm
Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm Open
In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete‐ and continuous‐time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of …
View article: Robust multiple stopping -- A path-wise duality approach
Robust multiple stopping -- A path-wise duality approach Open
In this paper we develop a solution method for general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model uncertainty, and fo…
View article: Optimal stopping via reinforced regression
Optimal stopping via reinforced regression Open
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each …
View article: Optimal Stopping of McKean--Vlasov Diffusions via Regression on Particle Systems
Optimal Stopping of McKean--Vlasov Diffusions via Regression on Particle Systems Open
In this paper we study optimal stopping problems for nonlinear Markov processes driven by a McKean-Vlasov SDE and aim at solving them numerically by Monte Carlo. To this end we propose a novel regression algorithm based on the correspondin…
View article: Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm
Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm Open
In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm for approximating the value of a discrete and continuous time optimal stopping problem. We prove that in the discrete case the WSM algorithm leads to semi-tractability o…
View article: Optimal stopping of McKean-Vlasov diffusions via regression on particle\n systems
Optimal stopping of McKean-Vlasov diffusions via regression on particle\n systems Open
In this paper we study optimal stopping problems for nonlinear Markov\nprocesses driven by a McKean-Vlasov SDE and aim at solving them numerically by\nMonte Carlo. To this end we propose a novel regression algorithm based on the\ncorrespon…
View article: Projected Particle Methods for Solving McKean--Vlasov Stochastic Differential Equations
Projected Particle Methods for Solving McKean--Vlasov Stochastic Differential Equations Open
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The proje…
View article: Projected particle methods for solving McKean-Vlasov stochastic\n differential equations
Projected particle methods for solving McKean-Vlasov stochastic\n differential equations Open
We propose a novel projection-based particle method for solving the\nMcKean-Vlasov stochastic differential equations. Our approach is based on a\nprojection-type estimation of the marginal density of the solution in each time\nstep. The pr…
View article: Projected particle methods for solving McKean--Vlaslov equations
Projected particle methods for solving McKean--Vlaslov equations Open
We study a novel projection-based particle method to the solution of the corresponding McKean-Vlasov equation. Our approach is based on the projection-type estimation of the marginal density of the solution in each time step. The projectio…
View article: Regression based duality approach to optimal control with application to hydro electricity storage
Regression based duality approach to optimal control with application to hydro electricity storage Open
In this paper we consider the problem of optimal control of stochastic processes. We employ the dual martingale method brought forward in [Brown, Smith, and Sun, 2010]. The martingale constituting the solution of the dual problem is determ…
View article: Option pricing in affine generalized Merton models
Option pricing in affine generalized Merton models Open
In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be genera…
View article: Uniform approximation of the Cox-Ingersoll-Ross process
Uniform approximation of the Cox-Ingersoll-Ross process Open
The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) de…
View article: Forward-reverse EM algorithm for Markov chains: convergence and numerical analysis
Forward-reverse EM algorithm for Markov chains: convergence and numerical analysis Open
We develop a forward-reverse EM (FREM) algorithm for estimating parameters that determine the dynamics of a discrete time Markov chain evolving through a certain measurable state space. As a key tool for the construction of the FREM method…
View article: Uniform approximation of the CIR process via exact simulation at random times
Uniform approximation of the CIR process via exact simulation at random times Open
In this paper we uniformly approximate the trajectories of the Cox-Ingersoll-Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the ex…
View article: Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration
Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration Open
We introduce a multiple curve LIBOR framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. The dynamics of OIS and LIBOR rates are specified following the methodology o…