COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
The Cost of Achieving the Best Portfolio in Hindsight
Mathematics of Operations Research
The statistical adversary allows optimal money-making trading strategies
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Universal Portfolios With and Without Transaction Costs
Machine Learning - Special issue: computational learning theory, COLT '97
Efficient algorithms for universal portfolios
The Journal of Machine Learning Research
Competitive algorithms for VWAP and limit order trading
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Online trading algorithms and robust option pricing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Prediction, Learning, and Games
Prediction, Learning, and Games
Improved second-order bounds for prediction with expert advice
Machine Learning
Optimal Algorithms for k-Search with Application in Option Pricing
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Can we learn to beat the best stock
Journal of Artificial Intelligence Research
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Universal portfolios with side information
IEEE Transactions on Information Theory
Minimax option pricing meets black-scholes in the limit
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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In this work, we extend the applicability of regret minimization to pricing financial instruments, following the work of [11]. More specifically, we consider pricing a type of exotic option called a fixed-strike lookback call option. A fixed-strike lookback call option has a known expiration time, at which the option holder has the right to receive the difference between the maximal price of a stock and some preagreed price. We derive upper bounds on the price of these options, assuming an arbitrage-free market, by developing two-way trading algorithms. We construct our trading algorithms by combining regret minimization algorithms and one-way trading algorithms. Our model assumes upper bounds on the absolute daily returns, overall quadratic variation, and stock price, otherwise allowing for fully adversarial market behavior.