On-Line Estimation of Hidden Markov Model Parameters
DS '00 Proceedings of the Third International Conference on Discovery Science
Internal Regret in On-Line Portfolio Selection
Machine Learning
Online trading algorithms and robust option pricing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Discrete denoising with shifts
IEEE Transactions on Information Theory
Regret minimization algorithms for pricing lookback options
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
Pricing exotic derivatives using regret minimization
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
A learning-based approach to reactive security
FC'10 Proceedings of the 14th international conference on Financial Cryptography and Data Security
Online portfolio selection: A survey
ACM Computing Surveys (CSUR)
| Hi-index | 0.06 |
For a market with m assets consider the minimum, over all possible sequences of asset prices through time n, of the ratio of the final wealth of a nonanticipating investment strategy to the wealth obtained by the best constant rebalanced portfolio computed in hindsight for that price sequence. We show that the maximum value of this ratio over all nonanticipating investment strategies is Vn[Σ2-nH(n1/n,...,nm/n)(n1!...nm!))] -1 where H(.) is the Shannon entropy, and we specify a strategy achieving it. The optimal ratio Vn is shown to decrease only polynomially in n, indicating that the rate of return of the optimal strategy converges uniformly to that of the best constant rebalanced portfolio determined with full hindsight. We also relate this result to the pricing of a new derivative security which might be called the hindsight allocation option.