John Schoenmakers
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
John Schoenmakers has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Christian Bayer
Weierstrass Institute, 10117 Berlin, Germany
3 shared publications - Denis Belomestny
Ph.D., Professor, University of Duisburg-Essen, Forsthausweg 247057 Duisburg, Germany
2 shared publications - Hilmar Mai1 shared publication
- Oleg Butkovsky
Weierstrass Institute, Berlin, Germany
1 shared publication - Paolo Pigato
Department of Economics and Finance, University of Rome Tor Vergata, Rome, Italy
1 shared publication - Paul P. Hager
Department of Mathematics Humboldt University Berlin Unter den Linden 6 10099 Berlin
1 shared publication
Latest Publications
- Open Access
- 7 August 2024
- Published by Springer Nature in Finance and Stochastics
- Vol. 28 (4) , 1147-1178
A reproducing kernel Hilbert space approach to singular local stochastic volatility McKean–Vlasov models
Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean–Vlasov equation $$ d X_{t}= \sigma (t,X_{t}) X_{t} \frac{\sqrt{v}_{t}}{\sqrt{\mathbb{E}[v_{t}|X_{t}]}}dW_{t}, $$ where $W$ is a Brownian motion and $v$ is an adapted diffusion process. This equation can be considered as a singular local stochastic volatility model. While such models are quite popular among practitioners, its well-posedness has unfortunately not yet been fully understood and in general is possibly not guaranteed at all. We develop a novel regularisation approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularised model is well posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularised model is able to perfectly replicate option prices coming from typical local volatility models. Our results are also applicable to more general McKean–Vlasov equations.- 7 August 2024
- Published by Springer Nature in Finance and Stochastics
- Vol. 28 (4) , 1147-1178
Open AccessA reproducing kernel Hilbert space approach to singular local stochastic volatility McKean–Vlasov models
Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean–Vlasov equation $$ d X_{t}= \sigma (t,X_{t}) X_{t} \frac{\sqrt{v}_{t}}{\sqrt{\mathbb{E}[v_{t}|X_{t}]}}dW_{t}, $$ where $W$ is a Brownian motion and $v$ is an adapted diffusion process. This equation can be considered as a singular local stochastic volatility model. While such models are quite popular among practitioners, its well-posedness has unfortunately not yet been fully understood and in general is possibly not guaranteed at all. We develop a novel regularisation approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularised model is well posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularised model is able to perfectly replicate option prices coming from typical local volatility models. Our results are also applicable to more general McKean–Vlasov equations. - Open Access
Reinforced optimal control
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 by linear least squares regression. Hence, the choice of basis functions is crucial for the accuracy of the method. Earlier work by some of us [Belomestny, Schoenmakers, Spokoiny, Zharkynbay. Commun.~Math.~Sci., 18(1):109-121, 2020](arXiv:1808.02341) proposes to reinforce the basis functions in the case of optimal stopping problems by already computed value functions for later times, thereby considerably improving the accuracy with limited additional computational cost. We extend the reinforced regression method to a general class of stochastic control problems, while considerably improving the method's efficiency, as demonstrated by substantial numerical examples as well as theoretical analysis.
Open AccessReinforced optimal control
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 by linear least squares regression. Hence, the choice of basis functions is crucial for the accuracy of the method. Earlier work by some of us [Belomestny, Schoenmakers, Spokoiny, Zharkynbay. Commun.~Math.~Sci., 18(1):109-121, 2020](arXiv:1808.02341) proposes to reinforce the basis functions in the case of optimal stopping problems by already computed value functions for later times, thereby considerably improving the accuracy with limited additional computational cost. We extend the reinforced regression method to a general class of stochastic control problems, while considerably improving the method's efficiency, as demonstrated by substantial numerical examples as well as theoretical analysis.
- Open Access
Forward-reverse EM algorithm for Markov chains: convergence and numerical analysis
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 we develop forward-reverse representations for Markov chains conditioned on a certain terminal state. These representations may be considered as an extension of the earlier work Bayer and Schoenmakers [2013] on conditional diffusions. We proof almost sure convergence of our algorithm for a Markov chain model with curved exponential family structure. On the numerical side we give a complexity analysis of the forward-reverse algorithm by deriving its expected cost. Two application examples are discuss to demonstrate the scope of possible applications ranging from models based on continuous time processes to discrete time Markov chain models.
Open AccessForward-reverse EM algorithm for Markov chains: convergence and numerical analysis
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 we develop forward-reverse representations for Markov chains conditioned on a certain terminal state. These representations may be considered as an extension of the earlier work Bayer and Schoenmakers [2013] on conditional diffusions. We proof almost sure convergence of our algorithm for a Markov chain model with curved exponential family structure. On the numerical side we give a complexity analysis of the forward-reverse algorithm by deriving its expected cost. Two application examples are discuss to demonstrate the scope of possible applications ranging from models based on continuous time processes to discrete time Markov chain models.