Optimal Buy-and-Hold Strategies for Financial Markets with Bounded Daily Returns

Chen, Gen-Huey; Kao, Ming-Yang; Lyuu, Yuh‐Dauh; Wong, Hsing-Kuo

doi:10.1137/s0097539799358847

Cited by 32 publications

(33 citation statements)

References 16 publications

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“…The online search problem is very similar to that of the one-way trading problem [8,11,12]. In fact, one-way trading can be seen as randomized searching.…”

Section: Introductionmentioning

confidence: 99%

A comparison of performance measures via online search

Boyar

Larsen

Maiti

2014

Theoretical Computer Science

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Though competitive analysis has been a very useful performance measure for the quality of online algorithms, it is recognized that it sometimes fails to distinguish between algorithms of different quality in practice. A number of alternative measures have been proposed, but, with a few exceptions, these have generally been applied only to the online problem they were developed in connection with. Recently, a systematic study of performance measures for online algorithms was initiated [Boyar, Irani, Larsen: Eleventh International Algorithms and Data Structures Symposium 2009], first focusing on a simple server problem. We continue this work by studying a fundamentally different online problem, online search, and the Reservation Price Policies in particular. The purpose of this line of work is to learn more about the applicability of various performance measures in different situations and the properties that the different measures emphasize. We investigate the following analysis techniques: Competitive, Relative Worst Order, Bijective, Average, Relative Interval, Random Order, and Max/Max. In addition to drawing conclusions on this work, we also investigate the measures' sensitivity to integral vs. real-valued domains, and as a part of this work, generalize some of the known performance measures. Finally, we have established the first optimality proof for Relative Interval Analysis.

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“…The online search problem is very similar to that of the one-way trading problem [8,11,12]. In fact, one-way trading can be seen as randomized searching.…”

Section: Introductionmentioning

confidence: 99%

A comparison of performance measures via online search

Boyar

Larsen

Maiti

2014

Theoretical Computer Science

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“…More recently, Fujiwara et al [11] have studied the one-way trading problem under the assumption that the input prices follow some given probability distribution. In [8], Chen et al introduced the planning game problem, which is similar to the one-way trading problem, and they gave an algorithm for their problem which imposes some different constraint on the prices: instead of assuming that p i ∈ [m, M ] for some price range [m, M ], their algorithm assumes that the difference between any two consecutive prices p i and p i+1 is not too large, or more precisely, they assumed that for any i, p i /β ≤ p i+1 ≤ αp i for some fixed α, β > 1. They showed that if there are n buyers, their algorithm has competitive ratio nαβ−(n−1)(α+β)+(n−2) αβ−1 .…”

Section: Previous Resultsmentioning

confidence: 99%

Competitive Algorithms for Unbounded One-Way Trading

Chin

Fu²,

Jiang

et al. 2014

Algorithmic Aspects in Information and Management

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In the one-way trading problem, a seller has L units of product to be sold to a sequence σ of buyers u 1 , u 2 , . . . , u σ arriving online and he needs to decide, for each u i , the amount of product to be sold to u i at the then-prevailing market price p i . The objective is to maximize the seller's revenue. We note that all previous algorithms for the problem need to impose some artificial upper bound M and lower bound m on the market prices, and the seller needs to know either the values of M and m, or their ratio M/m, at the outset.This paper gives a one-way trading algorithm that does not impose any bounds on market prices and whose performance guarantee depends directly on the input. In particular, we give a class of one-way trading algorithms such that for any positive integer h and any positive number ϵ, we have an algorithm A h,ϵ that has competitive ratio O(log r * (log (2) r * ) . . . (log (h−1) r * )(log (h) r * ) 1+ϵ ) if the value of r * = p * /p 1 , the ratio of the highest market price p * = max i p i and the first price p 1 , is large and satisfies log (h) r * > 1, where log (i) x denotes the application of the logarithm function i times to x ; otherwise, A h,ϵ has a constant competitive ratio Γ h . We also show that our algorithms are near optimal by showing that given any positive integer h and any one-way trading algorithm A, we can construct a sequence of buyers σ with log (h) r * > 1 such that the ratio between the optimal revenue and the revenue obtained by A is Ω(log r * (log (2) r * ) . . . (log (h−1) r * )(log (h) r * )). A special case of the one-way trading is also studied, in which the L units of product is comprised of L items, each of which must be sold atomically (or equivalently, the amount of product sold to each buyer must be an integer).Furthermore, a complementary problem to the one-way trading problem, say, the oneway buying problem, is studied in this paper. In the one-way buying problem, a buyer wants to purchase one unit of product through a sequence of n sellers v 1 , v 2 , . . . , v n arriving online, and she needs to decide the fraction to purchase from each v i at the then-prevailing market price p i . Her objective is to minimize the cost. The optimal competitive algorithms whose performance guarantees depend only on the lowest market price p * = min i p i , and one of M and φ, the price fluctuation ratio, are presented.

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“…yen) so as to maximize her final payoff while the price (or exchange rate from dollar to yen) varies unpredictably. There is a known simple transformation of (randomized) online search to (deterministic) one-way trading [2,[5][6][7]: The budget corresponds to probability 1 and exchanging some fraction of money (in deterministic one-way trading) means to stop the game with exactly that probability (in randomized online search) [5,7]. El-Yaniv et al suggested optimal solutions for several slight variants of the online search problem in which the upper/lower bounds of prices are constants and known a priori to the player [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…Since the optimal solutions for these variants are quite simple computationally (that is, the amounts to exchange are easy to compute, but the analysis is quite sophisticated), practical issues can be transformed to online search in order to find optimal solutions [8][9][10]. Chen et al suggested another variant of the problem in which the next price r depends on the current price r in a geometric manner: r/θ ≤ r ≤ rθ , where θ > 1 is the daily fluctuation ratio [2]. For the variant, these authors presented closed-form solutions to the competitive ratio.…”

Section: Introductionmentioning

confidence: 99%

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Online Search with Time-Varying Price Bounds

Damaschke

Tsigas

2007

Algorithmica

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Online search is a basic online problem. The fact that its optimal deterministic/randomized solutions are given by simple formulas (however with difficult analysis) makes the problem attractive as a target to which other practical online problems can be transformed to find optimal solutions. However, since the upper/lower bounds of prices in available models are constant, natural online problems in which these bounds vary with time do not fit in the available models.We present two new models where the bounds of prices are not constant but vary with time in certain ways. The first model, where the upper and lower bounds of (logarithmic) prices have decay speed, arises from a problem in concurrent data structures, namely to maximize the (appropriately defined) freshness of data in concurrent objects. For this model we present an optimal deterministic algorithm with competitive ratio √ D, where D is the known duration of the game, and a nearly-optimal randomized algorithm with competitive ratio. We also prove that the lower bound of competitive ratios of randomized algorithms is asymptotically ln D .The second model is inspired by the fact that some applications do not utilize the decay speed of the lower bound of prices in the first model. In the second model, only the upper bound decreases arbitrarily with time and the lower bound is constant. Clearly, the lower bound of competitive ratios proved for the first model holds also against the stronger adversary in the second model. For the second model, we present an optimal randomized algorithm. Our numerical experiments on the freshness problem show that this new algorithm achieves much better/smaller competitive ratios than previous algorithms do, for instance 2.25 versus 3.77 for D = 128.

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Optimal Buy-and-Hold Strategies for Financial Markets with Bounded Daily Returns

Cited by 32 publications

References 16 publications

A comparison of performance measures via online search

A comparison of performance measures via online search

Competitive Algorithms for Unbounded One-Way Trading

Online Search with Time-Varying Price Bounds

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