294 research outputs found
Collective Free Lunch and the FTAP
No full textThis paper extends the analysis presented in “Collective Arbitrage and the Value of Cooperation” by Biagini, Doldi, Fouque, Frittelli, and Meyer-Brandis (Finance and Stochastics 2025) to a general semimartingale market setting. We introduce the novel concept of a Collective Free Lunch and investigate the implications of the No Collective Free Lunch assumption within this framework. Furthermore, we establish the corresponding Fundamental Theorem of Asset Pricing and the pricing-hedging duality for general semimartingale markets
No arbitrage and preferences
No full textWe show that the classical concepts of No Arbitrage (NA) and of No Free Lunch with Vanishing Risk (NFLVR) are intimately linked with the preferences of the agents acting in the market. We point out that the difference, from an economic perspective, between NA and NFLVR rests on selection of the class of monotone, respectively monotone and concave, utility functions that determines the absence of a Market Free Lunch (MFL), a concept introduced in Frittelli 2004. We finally prove the equivalence between the absence of MLF and the existence of an equivalent sigma -martingale measure
On entropy martingale optimal transport theory
No full textIn this paper, we give an overview of (nonlinear) pricing-hedging duality and of its connection with the theory of entropy martingale optimal transport (EMOT), recently developed, and that of convex risk measures. Similarly to Doldi and Frittelli (Finance Stoch 27(2):255-304, 2023), we here establish a duality result between a convex optimal transport and a utility maximization problem. Differently from Doldi and Frittelli (Finance Stoch 27(2):255-304, 2023), we provide here an alternative proof that is based on a compactness assumption. Subhedging and superhedging can be obtained as applications of the duality discussed above. Furthermore, we provide a dual representation of the generalized optimized certainty equivalent associated with indirect utility
Frittelli-Martin Duo, April 18, 1985
No full textThis is the concert program of the Frittelli-Martin Duo performance on Thursday, April 18, 1985 at 3:00 p.m., at the Marshall Room, 855 Commonwealth Avenue. Works performed were Sonata in A major by Antonio Vivaldi, Sonata in A major, K. 526 by Wolfgang Amadeus Mozart, Sonata for Violin and Piano by Claude Debussy, and Sonata in D minor, Op. 108 by Johannes Brahms. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund
Real-valued systemic risk measures
No full textWe describe the axiomatic approach to real-valued Systemic Risk Measures, which is a natural counterpart to the nowadays classical univariate theory initiated by Artzner et al. in the seminal paper “Coherent measures of risk”, Math. Finance, (1999). In particular, we direct our attention towards Systemic Risk Measures of shortfall type with random allocations, which consider as eligible, for securing the system, those positions whose aggregated expected utility is above a given threshold. We present duality results, which allow us to motivate why this particular risk measurement regime is fair for both the single agents and the whole system at the same time. We relate Systemic Risk Measures of shortfall type to an equilibrium concept, namely a Systemic Optimal Risk Transfer Equilibrium, which conjugates Bühlmann’s Risk Exchange Equilibrium with a capital allocation problem at an initial time. We conclude by presenting extensions to the conditional, dynamic framework. The latter is the suitable setup when additional information is available at an initial time
The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets
No full textLet χ be a family of stochastic processes on a given filtered probability space (Ω, "F", ("F" "t" )"t" is an element of "T" , "P") with "T"⊆R + . Under the assumption that the set "M" "e" of equivalent martingale measures for χ is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to "P", in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy. Copyright Blackwell Publishers, Inc. 2000.
SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS
No full textWe introduce the notion of a Market Free Lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize No Arbitrage (NA) and No Free Lunch with Vanishing Risk (NFLVR) in terms of the Market Free Lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, resp. monotone and continuous, utility functions that determines the absence of the Market Free Lunch.
We also provide a direct proof of the equivalence between the absence of a Market Free Lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure
Dominated families of martingale, supermartingale and quasimartingale laws
No full textAbstractConsider a dominated family L of probability measures; we investigate the question of whether a single probability Q̂ ϵ L equivalent to the whole family L exists. We show that for supermartingale, quasimartingale and martingale laws the answer is positive. We then provide a necessary and sufficient condition for the existence of an equivalent (super, quasi) martingale measure and deduce an alternative characterization of semimartingales. We further study this problem in the context of security markets models and generalize the well-known fundamental theorem of asset pricing to cover the case of markets with frictions
Law Invariant Convex Risk Measures
No full textAs a generalization of a result by Kusuoka (2001), we provide the representation of law invariant convex risk measures. Very particular cases of law invariant coherent and convex risk measures are also studied
Conditional Systemic Risk Measures
No full textWe investigate to which extent the relevant features of (static) Systemic Risk Measures can be ex- tended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall Systemic Risk Measures. In the particular case of exponential preferences, we provide explicit formulas that also allow us to show a time consistency property. Finally, we provide an interpretation of the allocations associated to Conditional Shortfall Systemic Risk Measures as suitably defined equilibria. Conceptually, the generalization from static to conditional Systemic Risk Measures can be achieved in a natural way, even though the proofs become more technical than in the unconditional framework
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