On complete securities markets and the martingale property of securities prices

Müller, Sigrid

doi:10.1016/0165-1765(89)90108-0

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…shown by a counterexample in [20]. By [15] we obtain that L(Z) must be the largest class of integrands over which multidimensional integrals with respect to Z can be defined, as done implicitly in [11].…”

Section: Remark 13 In Theorem 12 the Definition Of The Space L(z) Is Crucial Asmentioning

confidence: 96%

Second Fundamental Theorem of Asset Pricing

Biagini

2010

Encyclopedia of Quantitative Finance

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The second fundamental theorem of asset pricing (in short, sft) concerns the mathematical characterization of the economic concept of market completeness for liquid and frictionless markets with an arbitrary number of assets. The theorem establishes the mathematical necessary and sufficient conditions in order to guarantee that every contingent claim on the market can be duplicated with a portfolio of primitive assets. For finite assets economies, completeness (i.e. perfect replication of every claim on the market by admissible self-financing strategies) is equivalent to uniqueness of the equivalent martingale measure. This result can be extended to market models with an infinite number of assets by defining completeness in terms of approximate replication of claims by attainable ones.

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Section: Remark 13 In Theorem 12 the Definition Of The Space L(z) Is Crucial Asmentioning

confidence: 96%

Second Fundamental Theorem of Asset Pricing

Biagini

2010

Encyclopedia of Quantitative Finance

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“…In the general semimartingale framework, the equivalence of the uniqueness of an EMM and the completeness of a market model were conjectured by Harrison and Pliska [13,14] (see also [18]). The case of the Brownian filtration is examined in [16].…”

Section: Completeness Of the Multidimensional Black And Scholes Modelmentioning

confidence: 97%

“…It follows from the Itô formula that the discounted stock price (18) for any i = 1, . It follows from the Itô formula that the discounted stock price (18) for any i = 1, .…”

Section: Multidimensional Black and Scholes Modelmentioning

confidence: 99%

Complete Markets

Rutkowski¹

2010

Encyclopedia of Quantitative Finance

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A market model is said to be complete if any financial derivative admits a replicating strategy. The completeness of a market model ensures that any derivative security can be priced by arbitrage and hedged through dynamic trading in primary traded assets. In a complete market model, not only call and put options but also any exotic option can be replicated by dynamic trading in the primary securities. The Cox, Ross, and Rubinstein binomial model of the stock price is complete. The classic Black and Scholes options pricing model enjoys the property of completeness under suitable technical assumptions

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“…In their seminal papers Harrison and Pliska clearly state that completeness is a joint property of the filtration and of the asset price process and in particular they argued that the structure of the filtration should influence completeness. They also provided the original version of the II Theorem of Asset Pricing (see [18], [19]), even if their statement is not completely correct in the definition of self-financial strategies (to clarify this fact see [31] and the Appendix in [23] and [7] about the distinction between vector completeness and component completeness, which is at the origin of the imprecision of the Harrison and Pliska's result). Completeness has been widely studied when the reference filtration coincides with the natural one.…”

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confidence: 99%

Enlargement of filtration and predictable representation property for semi-martingales

Calzolari

Torti

2015

Stochastics

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We present two examples of loss of the predictable representation property for semi-martingales by enlargement of the reference filtration. First of all we show that the predictable representation property for a semi-martingale X does not transfer from the reference filtration F to a larger filtration G if the information starts growing up to a positive time. Then we study the case G = F ∨ H when there exists a second special semi-martingale Y enjoying the predictable representation property with respect to H. We establish conditions under which the triplet (X, Y, [X, Y ]) enjoys the predictable representation property with respect to G.

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On complete securities markets and the martingale property of securities prices

Cited by 9 publications

References 10 publications

Second Fundamental Theorem of Asset Pricing

Second Fundamental Theorem of Asset Pricing

Complete Markets

Enlargement of filtration and predictable representation property for semi-martingales

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