2,799 research outputs found
Bounding Optimality Gap in Stochastic Optimization via Bagging: Statistical Efficiency and Stability
We study a statistical method to estimate the optimal value, and the
optimality gap of a given solution for stochastic optimization as an assessment
of the solution quality. Our approach is based on bootstrap aggregating, or
bagging, resampled sample average approximation (SAA). We show how this
approach leads to valid statistical confidence bounds for non-smooth
optimization. We also demonstrate its statistical efficiency and stability that
are especially desirable in limited-data situations, and compare these
properties with some existing methods. We present our theory that views SAA as
a kernel in an infinite-order symmetric statistic, which can be approximated
via bagging. We substantiate our theoretical findings with numerical results
From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments
We consider a non-stochastic online learning approach to price financial
options by modeling the market dynamic as a repeated game between the nature
(adversary) and the investor. We demonstrate that such framework yields
analogous structure as the Black-Scholes model, the widely popular option
pricing model in stochastic finance, for both European and American options
with convex payoffs. In the case of non-convex options, we construct
approximate pricing algorithms, and demonstrate that their efficiency can be
analyzed through the introduction of an artificial probability measure, in
parallel to the so-called risk-neutral measure in the finance literature, even
though our framework is completely adversarial. Continuous-time convergence
results and extensions to incorporate price jumps are also presented
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