32 research outputs found
Sequential Design for Ranking Response Surfaces
We propose and analyze sequential design methods for the problem of ranking
several response surfaces. Namely, given response surfaces over a
continuous input space , the aim is to efficiently find the index of
the minimal response across the entire . The response surfaces are not
known and have to be noisily sampled one-at-a-time. This setting is motivated
by stochastic control applications and requires joint experimental design both
in space and response-index dimensions. To generate sequential design
heuristics we investigate stepwise uncertainty reduction approaches, as well as
sampling based on posterior classification complexity. We also make connections
between our continuous-input formulation and the discrete framework of pure
regret in multi-armed bandits. To model the response surfaces we utilize
kriging surrogates. Several numerical examples using both synthetic data and an
epidemics control problem are provided to illustrate our approach and the
efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic Environments
This paper studies the portfolio optimization problem when the investor's
utility is general and the return and volatility of the risky asset are fast
mean-reverting, which are important to capture the fast-time scale in the
modeling of stock price volatility. Motivated by the heuristic derivation in
[J.-P. Fouque, R. Sircar and T. Zariphopoulou, \emph{Mathematical Finance},
2016], we propose a zeroth order strategy, and show its asymptotic optimality
within a specific (smaller) family of admissible strategies under proper
assumptions. This optimality result is achieved by establishing a first order
approximation of the problem value associated to this proposed strategy using
singular perturbation method, and estimating the risk-tolerance functions. The
results are natural extensions of our previous work on portfolio optimization
in a slowly varying stochastic environment [J.-P. Fouque and R. Hu, \emph{SIAM
Journal on Control and Optimization}, 2017], and together they form a whole
picture of analyzing portfolio optimization in both fast and slow environments