17,277 research outputs found
Coupling Index and Stocks
In this paper, we are interested in continuous time models in which the index
level induces some feedback on the dynamics of its composing stocks. More
precisely, we propose a model in which the log-returns of each stock may be
decomposed into a systemic part proportional to the log-returns of the index
plus an idiosyncratic part. We show that, when the number of stocks in the
index is large, this model may be approximated by a local volatility model for
the index and a stochastic volatility model for each stock with volatility
driven by the index. This result is useful in a calibration perspective : it
suggests that one should first calibrate the local volatility of the index and
then calibrate the dynamics of each stock. We explain how to do so in the
limiting simplified model and in the original model
Finding Any Nontrivial Coarse Correlated Equilibrium Is Hard
One of the most appealing aspects of the (coarse) correlated equilibrium
concept is that natural dynamics quickly arrive at approximations of such
equilibria, even in games with many players. In addition, there exist
polynomial-time algorithms that compute exact (coarse) correlated equilibria.
In light of these results, a natural question is how good are the (coarse)
correlated equilibria that can arise from any efficient algorithm or dynamics.
In this paper we address this question, and establish strong negative
results. In particular, we show that in multiplayer games that have a succinct
representation, it is NP-hard to compute any coarse correlated equilibrium (or
approximate coarse correlated equilibrium) with welfare strictly better than
the worst possible. The focus on succinct games ensures that the underlying
complexity question is interesting; many multiplayer games of interest are in
fact succinct. Our results imply that, while one can efficiently compute a
coarse correlated equilibrium, one cannot provide any nontrivial welfare
guarantee for the resulting equilibrium, unless P=NP. We show that analogous
hardness results hold for correlated equilibria, and persist under the
egalitarian objective or Pareto optimality.
To complement the hardness results, we develop an algorithmic framework that
identifies settings in which we can efficiently compute an approximate
correlated equilibrium with near-optimal welfare. We use this framework to
develop an efficient algorithm for computing an approximate correlated
equilibrium with near-optimal welfare in aggregative games.Comment: 21 page
- …