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33
COHERENT MULTIPERIOD RISK ADJUSTED VALUES AND BELLMAN’S PRINCIPLE
, 2004
"... Starting with a time0 coherent risk measure defined for “value processes”, we define, also at intermediate times, a risk measurement process. Two other constructions of such measurement processes are given in terms of sets of test probabilities. These constructions are identical and related to the ..."
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Cited by 108 (7 self)
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Starting with a time0 coherent risk measure defined for “value processes”, we define, also at intermediate times, a risk measurement process. Two other constructions of such measurement processes are given in terms of sets of test probabilities. These constructions are identical and related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity in decisionmaking. We finally deduce risk measurements for final value of lockedin positions and repeat a warning concerning TailValueatrisk.
Dynamic Monetary Risk Measures for Bounded DiscreteTime Processes
, 2004
"... We study timeconsistency questions for processes of monetary risk measures that depend on bounded discretetime processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures timeconsistent if it assigns to a process ..."
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Cited by 98 (8 self)
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We study timeconsistency questions for processes of monetary risk measures that depend on bounded discretetime processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures timeconsistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time, and we show how this property manifests itself in the corresponding process of acceptance sets. For processes of coherent and convex monetary risk measures admitting a robust representation with sigmaadditive linear functionals, we give necessary and sufficient conditions for timeconsistency in terms of the representing functionals.
Pricing, Hedging and Optimally Designing Derivatives via Minimization of Risk Measures
 IN VOLUME ON INDIFFERENCE PRICING, PRINCETON UNIVERSITY PRESS. 24 BERNARDO A.E. AND LEDOIT O.,(2000
, 2005
"... The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in the literature to provide a satisfactory answer to this probl ..."
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Cited by 56 (5 self)
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The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in the literature to provide a satisfactory answer to this problem, for a particular choice criterion. Among them, Hodges and Neuberger [72] proposed in 1989 a method based on utility maximization. The price of the contingent claim is then obtained as the smallest (resp. largest) amount leading the agent indifferent between selling (resp. buying) the claim and doing nothing. The price obtained is the indifference seller's (resp. buyer's) price. Since then, many authors have used this approach, the exponential utility function being most often used (see for instance, El Karoui and Rouge [51], Becherer [11], Delbaen et al. [39] , Musiela and Zariphopoulou [93] or Mania and Schweizer [89]...). In this chapter, we also adopt this exponential utility point of view to start with in order to nd the optimal hedge and price of a contingent claim based on a nontradable risk. But soon, we notice that the right framework to work with is not that of the exponential utility itself but that of the certainty equivalent which is a convex functional satisfying some nice properties among which that of cash translation invariance. Hence, the results obtained in this particular framework can be immediately extended to functionals satisfying the same properties, in other words to convex risk measures as introduced by Föllmer and Schied [53] and [54]
Time consistency conditions for acceptability measures with an application to Tail Value at Risk
 Insurance: Mathematics and Economics
, 2007
"... An acceptability measure is a number that summarizes information on monetary outcomes of a given position in various scenarios, and that, depending on context, may be interpreted as a capital requirement or as a price. In a multiperiod setting, it is reasonable to require that an acceptability meas ..."
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Cited by 15 (5 self)
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An acceptability measure is a number that summarizes information on monetary outcomes of a given position in various scenarios, and that, depending on context, may be interpreted as a capital requirement or as a price. In a multiperiod setting, it is reasonable to require that an acceptability measure should satisfy certain conditions of time consistency. Various notions of time consistency may be considered. Within the framework of coherent risk measures as proposed by Artzner et al. (1999), we establish implication relations between a number of different notions, and we determine how each notion of time consistency is expressed through properties of a representing set of test measures. We propose modifications of the standard TailValueatRisk measure that have stronger consistency properties than the original.
Timeconsistency of indifference prices and monetary utility functions
, 2005
"... We consider an economic agent with dynamic preference over a set of uncertain monetary payoffs. We assume that the agent’s preferences are given by utility functions, which are updated in a timeconsistent way as more information is becoming available. Our main result is that the agent’s indifferenc ..."
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Cited by 11 (0 self)
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We consider an economic agent with dynamic preference over a set of uncertain monetary payoffs. We assume that the agent’s preferences are given by utility functions, which are updated in a timeconsistent way as more information is becoming available. Our main result is that the agent’s indifference prices are timeconsistent if and only if his preferences can be represented with utility functions that are additive with respect to cash. We call such utility functions monetary. The proof is based on a characterization of timeconsistency of dynamic utility functions in terms of indifference sets. As a special case, we obtain the result that expected utility leads to timeconsistent indifference prices if and only if it is based on a linear or exponential function.
Recursiveness of indifference prices and translationinvariant preferences
, 2009
"... We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that preferences are updated in a timeconsistent way as more information is becoming available. Our main result is that the agent’s indifference prices are recursive if and only if the prefer ..."
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Cited by 9 (0 self)
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We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that preferences are updated in a timeconsistent way as more information is becoming available. Our main result is that the agent’s indifference prices are recursive if and only if the preferences are translationinvariant. The proof is based on a characterization of timeconsistency of dynamic preferences in terms of indifference sets. As a special case, we obtain that expected utility leads to recursive indifference prices if and only if absolute risk aversion is constant, that is, the Bernoulli utility function is linear or exponential.
Incomplete markets
 of Handbooks in Operations Research and Management Science
"... In reality, markets are incomplete, meaning that some payoffs cannot be replicated by trading in marketed securities. The classic noarbitrage theory of valuation in a complete market, based on the unique price of a selffinancing replicating portfolio, is not adequate for nonreplicable payoffs in i ..."
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Cited by 8 (1 self)
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In reality, markets are incomplete, meaning that some payoffs cannot be replicated by trading in marketed securities. The classic noarbitrage theory of valuation in a complete market, based on the unique price of a selffinancing replicating portfolio, is not adequate for nonreplicable payoffs in incomplete markets. We focus on pricing overthecounter derivative securities, surveying many proposed methodologies, drawing relationships between them, and evaluating their promise. 1
Pricing with coherent risk,
 Probability Theory and Its Applications
, 2007
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MATURITYINDEPENDENT RISK MEASURES
, 710
"... Abstract. The new notion of maturityindependent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion framework, that, surprisingly, some of the widely utilize ..."
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Cited by 4 (1 self)
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Abstract. The new notion of maturityindependent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion framework, that, surprisingly, some of the widely utilized risk measures cannot be used to build maturityindependent counterparts. We construct a large class of maturityindependent risk measures and give representative examples in both continuous and discretetime financial models. 1.