2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
MB5  Applications in statistics
May 16, 2022 03:30 PM – 05:10 PM
Location: LouisLaberge (red)
Chaired by Alexandre Roch
3 Presentations

03:30 PM  03:55 PM
Variance reduction techniques in optimal stopping
We compare the performance of variance reduction techniques such as control variates and importance sampling in the context of pricing Bermudian options.

03:55 PM  04:20 PM
Generate and predict multivariate time series
Time series forecasting is to try to predict future realizations based on past observations. Those predictions can be precise or probabilistic depending on the model. Recent development in machine learning has accelerated the quantity of interesting models. The model selection is very much dependent of the use case and needs a thorough investigation. It is however important to compare different models to measure their prediction quality, robustness, computational performance and data requirements. We will present a package written in Python to compare models. Multivariate time series from simulation and historical data will be used as the environment. Then, given a list of models, different metrics will be measure on the given environments.

04:20 PM  04:45 PM
Optimal ratcheting dividends policy with resets
A welldocumented feature of firms’ dividend policies in practice is that cash dividend payments to shareholders seldom decrease in time. Indeed, classical dividend signaling theory assumes that the action of decreasing the dividend to shareholders sends a negative signal to market participants implying reduced prospects and diminished performance. This issue has been addressed in the literature by restricting the set of admissible policies to only increasing ones, also called ratcheting strategies. However, an unanticipated consequence of ratcheting constraints is that the firm may end up putting itself in bankruptcy. In this paper, we relax the ratcheting constraint by allowing the firm to reduce its dividend rate. As this sends a negative signal to market participants, the result is that the equity value is assumed to be affected by such an action. We setup this problem as an optimal stochastic control problem and show that the value function (which depends on the current value of the equity and the current dividend rate) can be reduced to one dimension and that it is the unique viscosity solution of an associated HJB equation. We fully describe the optimal dividend policy in terms of the priceearnings ratio and provide numerical examples.