Second Fundamental Theorem of Asset Pricing

Biagini, Francesca

doi:10.1002/9780470061602.eqf04008

Cited by 11 publications

(14 citation statements)

References 25 publications

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“…This result holds irrespective of whether the market contains a finite or infinite number of assets. Similar statements can be found, e.g., in , as well as Biagini (2010). Hence, in every complete financial market we are always able to find a unique representation of asset prices and fair values.…”

Section: Completenesssupporting

confidence: 71%

“…9 For this reason, the requirements on {H t } that are mentioned by Harrison and Pliska (1981) are too strict (Jarrow and Madan, 1991). See also Remark 1.3 in Biagini (2010). 10 According to Delbaen and Schachermayer (1994, Definition 2.7), the strategy {H t } is called "a-admissible" if and only if t 0 H s dP s ≥ −a for a given number a > 0 but just "admissible" if and only if t 0 H s dP s ≥ −a for some a ≥ 0. a−V 0 numéraire assets at t = 0, we obtain the strategy H a t , which has a nonnegative discounted value process V a t with V a t = a + t 0 H a s dP s for all t ≥ 0.…”

Section: Preliminary Definitions and Assumptionsmentioning

confidence: 99%

“…For a nice overview of those contributions seeBiagini (2010). 2 As a consequence of the extended version of the 3 rd FTAP, which I present in this work, the discounted price processes…”

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confidence: 99%

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Pricing and Valuation Under the Real-World Measure

Frahm

2016

Int. J. Theor. Appl. Finan.

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In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices are typically expressed in terms of a risk-neutral measure. This makes it difficult to transfer the fundamental results of financial mathematics to econometrics. I show that the aforementioned problems evaporate if the financial market is complete and sensitive. In this case, after an appropriate choice of the numéraire, the discounted price processes turn out to be uniformly integrable martingales under the real-world measure. This leads to a Law of One Price and a simple real-world valuation formula in a model-independent framework where the number of assets as well as the lifetime of the market can be finite or infinite.

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Section: Completenesssupporting

confidence: 71%

Section: Preliminary Definitions and Assumptionsmentioning

confidence: 99%

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Pricing and Valuation Under the Real-World Measure

Frahm

2016

Int. J. Theor. Appl. Finan.

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“…Lemma A.1 in Appendix A shows that, in the market without model uncertainty, the above riskneutral default intensity is uniquely determined under a mild invertibility condition on the matrix of bond depreciations (see Lemma A.1 for the precise statement). By the Second Fundamental Theorem of Asset Pricing (see for example Theorem 1.2 in Biagini (2010)), this implies that the market model consisting of bank account and risky bonds is complete.…”

Section: The Portfolio Securitiesmentioning

confidence: 92%

Robust Optimization of Credit Portfolios

Bo¹,

Capponi²

2017

Mathematics of OR

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We introduce a dynamic credit portfolio framework where optimal investment strategies are robust against misspecifications of the reference credit model. The risk-averse investor models his fear of credit risk misspecification by considering a set of plausible alternatives whose expected log likelihood ratios are penalized. We provide an explicit characterization of the optimal robust bond investment strategy, in terms of default state dependent value functions associated with the max-min robust optimization criterion. The value functions can be obtained as the solutions of a recursive system of HJB equations. We show that each HJB equation is equivalent to a suitably truncated equation admitting a unique bounded regular solution. The truncation technique relies on estimates for the solution of the master HJB equation that we establish.

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“…The second fundamental theorem considers the more special case when a market is complete, i.e., when every European contingent claim can be replicated perfectly by a trading strategy, see [6] for an overview and literature. It characterizes completeness by uniqueness of the prices for claims.…”

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confidence: 99%

A conditional Version of the second fundamental theorem of asset pricing in discrete time

Niemann,

Schmidt

2024

FMF

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We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitragefree prices. Moreover, we characterize attainability and market completeness. We derive a conditional version of the second fundamental theorem of asset pricing, which, surprisingly, is not available up to now.The main tools we use are the time consistency properties of dynamic nonlinear expectations, which we apply to the super-and subhedging prices. The results obtained extend existing results in the literature, where the conditional setting is considered in most cases only on finite probability spaces.

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Second Fundamental Theorem of Asset Pricing

Cited by 11 publications

References 25 publications

Pricing and Valuation Under the Real-World Measure

Pricing and Valuation Under the Real-World Measure

Robust Optimization of Credit Portfolios

A conditional Version of the second fundamental theorem of asset pricing in discrete time

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