No asymptotic free lunch reviewed in the light of Orlicz spaces

Klein, Irene

doi:10.1007/978-3-540-77913-1_22

Cited by 5 publications

(4 citation statements)

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“…If NAFL holds then it is not possible to approximate a strictly positive profit in a weak-star sense by trading in any finite number of the given assets (although we can use more and more of them). Originally the notion NAFL was introduced in [23], see also [24]. Remark 4.3.…”

Section: Bond Markets As Large Financial Marketsmentioning

confidence: 99%

“…However, as there is a local martingale measure for all bond prices discounted by the numéraire, the general theorem about NAFL in large financial markets implies that for any large financial market (induced by the bond market via any sequence of maturities) NAFL holds. In particular NAFL follows from the existence of Q * by [23], [24].…”

Section: Global Existence Of An Equivalent Local Martingale Measurementioning

confidence: 99%

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When roll-overs do not qualify as numéraire: bond markets beyond short rate paradigms

Klein¹,

Schmidt²,

Teichmann³

2013

Preprint

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We investigate default-free bond markets where the standard relationship between a possibly existing bank account process and the term structure of bond prices is broken, i.e. the bank account process is not a valid numéraire. We argue that this feature is not the exception but rather the rule in bond markets when starting with, e.g., terminal bonds as numéraires.Our setting are general càdlàg processes as bond prices, where we employ directly methods from large financial markets. Moreover, we do not restrict price process to be semimartingales, which allows for example to consider markets driven by fractional Brownian motion. In the core of the article we relate the appropriate no arbitrage assumptions (NAFL), i.e. no asymptotic free lunch, to the existence of an equivalent local martingale measure with respect to the terminal bond as numéraire, and no arbitrage opportunities of the first kind (NAA1) to the existence of a supermartingale deflator, respectively. In all settings we obtain existence of a generalized bank account as a limit of convex combinations of roll-over bonds.Additionally we provide an alternative definition of the concept of a numéraire, leading to a possibly interesting connection to bubbles. If we can construct a bank account process through roll-overs, we can relate the impossibility of taking the bank account as numéraire to liquidity effects. Here we enter endogenously the arena of multiple yield curves.The theory is illustrated by several examples.1991 Mathematics Subject Classification. 60H30, 91G30. Key words and phrases. large financial markets, bond markets, interest rate theory, forward measure, short rate, bubble, numeraire.The authors thank ETH Foundation for its support of this research project. The first and second author thank the Forschungsinstitut Mathematik at ETH Zürich for its generous hospitality.

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Section: Bond Markets As Large Financial Marketsmentioning

confidence: 99%

Section: Global Existence Of An Equivalent Local Martingale Measurementioning

confidence: 99%

When roll-overs do not qualify as numéraire: bond markets beyond short rate paradigms

Klein¹,

Schmidt²,

Teichmann³

2013

Preprint

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“…Inspired by APM, an abstract framework for markets with "many" assets has been proposed in [14]. The theory of such "large financial markets" has been extensively investigated in [19,20,15,18,21,8,29,30,2,22,23,1,35,5,10]. There has also been a recent revival of interest in such models, see [25,6].…”

Section: Introductionmentioning

confidence: 99%

Maximizing expected utility in the Arbitrage Pricing Model

Rásonyi

2017

Journal of Mathematical Analysis and Applications

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“…Note that in [12], the weakly compact subsets of L 1 were described in a slightly different way. However, the short note [14] shows that the sets B F,n can be used instead of the sets K ϕ,n for [12]. In fact, the use of Orlicz space methods makes the proof for [12] more transparent.…”

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confidence: 99%

Market free lunch and large financial markets

Klein¹

2006

Ann. Appl. Probab.

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The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from the theory of Orlicz spaces. Moreover, various notions of no asymptotic arbitrage are characterized in terms of no asymptotic market free lunch; the difference lies in the set of utilities. In particular, it is shown directly that no asymptotic market free lunch with respect to monotone concave utilities is equivalent to no asymptotic free lunch. In principle, the paper can be seen as the large financial market analogue of [Math. Finance 14 (2004) 351--357] and [Math. Finance 16 (2006) 583--588].Comment: Published at http://dx.doi.org/10.1214/105051606000000484 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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No asymptotic free lunch reviewed in the light of Orlicz spaces

Cited by 5 publications

References 19 publications

When roll-overs do not qualify as numéraire: bond markets beyond short rate paradigms

When roll-overs do not qualify as numéraire: bond markets beyond short rate paradigms

Maximizing expected utility in the Arbitrage Pricing Model

Market free lunch and large financial markets

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