Additive portfolio improvement and utility-efficient payoffs

Kassberger, Stefan; Liebmann, Thomas

doi:10.1007/s11579-016-0179-3

Cited by 6 publications

(8 citation statements)

References 25 publications

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“…The following result in Kassberger and Liebmann (2017), Proposition 6, characterizes the generalized

\bar{NSA}

‐condition by showing that this notion is equivalent to

scriptG

‐measurability of

dZ = \frac{dQ}{dP}

. Proposition Let

Q \sim P

be an equivalent pricing measure.…”

Section: Generalized Statistical Scriptg‐arbitrage Strategiesmentioning

confidence: 99%

“…The following result in Kassberger and Liebmann (2017), Proposition 6, characterizes the generalized NSA-condition by showing that this notion is equivalent to -measurability of dZ = The proof of this result is achieved by Jensen's inequality and using as candidate of a generalized -arbitrage…”

Section: Generalized Statistical -Arbitrage Strategiesmentioning

confidence: 99%

“…For risk and investment optimization problems it has been shown that conditioning of payoffs on the pricing density leads to improved (cost efficient) payoffs (see Burgert & Rüschendorf, 2006, Kassberger and Liebmann (2017) and several papers cited therein). In connection with these improvement procedures, Kassberger and Liebmann (2017) introduced, in the case where one pricing measure

Q

is specified, the following notion of generalized statistical

scriptG

‐arbitrage for a general static payoff

X

considered as a generalized strategy. Note that in their context no financial market is specified,

Q

is any probability measure dominated by

P

.…”

Section: Generalized Statistical Scriptg‐arbitrage Strategiesmentioning

confidence: 99%

“…Investigating in detail a class of trinomial models we find that the converse direction in Bondarenko's equivalence theorem is not valid in general. Kassberger and Liebmann (2017) introduced and characterized statistical

scriptG

‐arbitrage w.r.t. generalized (static) strategies in the case where one pricing measure is fixed.…”

Section: Introductionmentioning

confidence: 99%

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Generalized statistical arbitrage concepts and related gain strategies

Rein

Rüschendorf

Schmidt

2021

Mathematical Finance

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The notion of statistical arbitrage introduced in Bondarenko (2003) is generalized to statistical-arbitrage corresponding to trading strategies which yield positive gains on average in a class of scenarios described by a-algebra. This notion contains classical arbitrage as a special case. Admitting general static payoffs as generalized strategies, as done in Kassberger and Liebmann (2017) in the case of one pricing measure, leads to the notion of generalized statistical-arbitrage. We show that even under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios. In the first part of the paper we prove that the characterization in Bondarenko (2003), no statistical arbitrage being equivalent to the existence of an equivalent local martingale measure with a path-independent density, is not correct in general. We establish that this equivalence holds true in complete markets and we derive a general sufficient condition for statistical-arbitrages. As a main result we derive the equivalence of no statistical-arbitrage to no generalized statistical-arbitrage. In the second part of the paper we construct several classes of profitable generalized strategies with respect to various choices of the-algebra. In particular, we consider several forms This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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“…The following result in Kassberger and Liebmann (2017), Proposition 6, characterizes the generalized

\bar{NSA}

‐condition by showing that this notion is equivalent to

scriptG

‐measurability of

dZ = \frac{dQ}{dP}

. Proposition Let

Q \sim P

be an equivalent pricing measure.…”

Section: Generalized Statistical Scriptg‐arbitrage Strategiesmentioning

confidence: 99%

Section: Generalized Statistical -Arbitrage Strategiesmentioning

confidence: 99%

Q

is specified, the following notion of generalized statistical

scriptG

‐arbitrage for a general static payoff

X

considered as a generalized strategy. Note that in their context no financial market is specified,

Q

is any probability measure dominated by

P

.…”

Section: Generalized Statistical Scriptg‐arbitrage Strategiesmentioning

confidence: 99%

scriptG

‐arbitrage w.r.t. generalized (static) strategies in the case where one pricing measure is fixed.…”

Section: Introductionmentioning

confidence: 99%

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Generalized statistical arbitrage concepts and related gain strategies

Rein

Rüschendorf

Schmidt

2021

Mathematical Finance

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show abstract

“…This leads to the following notion of generalized statistical G -arbitrage strategies and the corresponding notion of generalized statistical G -arbitrage. This concept was used in several papers dealing with improvement procedures of financial contracts, see for example Kassberger and Liebmann (2017). We denote by L 1 (P, Q) := L 1 (P ) ∩ L 1 (Q) the set of random variables which are integrable with respect to P and Q.…”

Section: Generalized G -Arbitrage Strategiesmentioning

confidence: 99%

Generalized Statistical Arbitrage Concepts and Related Gain Strategies

2019

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Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via an information system given by a σ-algebra and so this notion contains classical arbitrage as a special case. It also covers the notion of statistical arbitrage introduced in Bondarenko (2003).Relaxing these notions further we introduce generalized profitable strategies which include also static or semi-static strategies. Under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios.In the first part of the paper we characterize these generalized statistical no-arbitrage notions. In the second part of the paper we construct several profitable generalized strategies with respect to various choices of the information system. In particular, we consider several forms of embedded binomial strategies and follow-the-trend strategies as well as partition-type strategies. We study and compare their behaviour on simulated data. Additionally, we find good performance on market data of these simple strategies which makes them profitable candidates for real applications. arXiv:1907.09218v2 [q-fin.MF]

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Robust statistical arbitrage strategies

Lütkebohmert

Sester

2020

Quantitative Finance

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Additive portfolio improvement and utility-efficient payoffs

Cited by 6 publications

References 25 publications

Generalized statistical arbitrage concepts and related gain strategies

Generalized statistical arbitrage concepts and related gain strategies

Generalized Statistical Arbitrage Concepts and Related Gain Strategies

Robust statistical arbitrage strategies

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