arXiv subjects

John G. M. Schoenmakers

Publications and source records attributed to John G. M. Schoenmakers.

3 recordsLinked to original sources

arXiv2026

Optimal Stopping with Randomly Arriving Stopping Opportunities

We develop simulation-based methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in a wide variety of applications with market frictions, such as limited liquidity, incomplete information and transaction costs. Our approach employs random time scales to map the original problem to an integer-time stopping problem with (possibly) infinite horizon. We introduce an infinite-horizon policy iteration algorithm to generate lower-biased estimates of the value function and establish a martingale dual representation to generate upper-biased estimates. Furthermore, we extend a family of backward dynamic programming methods that includes least-squares Monte Carlo. We illustrate the performance of our methods, their general applicability and the managerial implications of randomly arriving opportunities to stop in three examples: a stopped jump-diffusion that can be analyzed in closed form, a random-exercise version of a multi-dimensional max-call contract, and a real options problem in an illiquid market.

math.PR↗

arXiv2021

Robust Multiple Stopping -- A Pathwise Duality Approach

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 uncertainty, and for general reward processes driven by multi-dimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appealing pathwise optimality (i.e., almost sure) properties. Next, we exploit these theoretical results to develop upper and lower bounds that, as we formally show, not only converge to the true solution asymptotically, but also constitute genuine pre-limiting upper and lower bounds. We illustrate the applicability of our approach in a few examples and analyze the impact of model uncertainty on optimal multiple stopping strategies.

math.PR↗

arXiv2012

Libor model with expiry-wise stochastic volatility and displacement

We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-strike panel at the market. However, since even after freezing the Libors in the drift of this model, the Libor dynamics are not affine, new affine approximations have to be developed in order to obtain Fourier based (approximate) pricing procedures for caps and swaptions. As a result, we end up with a Libor modeling package that allows for efficient calibration to a complete system of cap/swaption market quotes that performs well even in crises times, where structural breaks in vola-strike-maturity panels are typically observed.

q-fin.PR↗