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Using duality methods, we prove several key properties of the indifference price π for contingent claims. The underlying market model is very general and the mathematical formulation is based on a duality naturally induced by the problem. In particular, the indifference price π turns out to be a convex risk measure on the Orlicz space induced by the utility function. 相似文献
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Marco Frittelli 《Mathematical Finance》2000,10(1):39-52
Let χ be a family of stochastic processes on a given filtered probability space (Ω, F, (Ft)t∈T, P) with T?R+. Under the assumption that the set Me 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. 相似文献
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Francesca Biagini Jean‐Pierre Fouque Marco Frittelli Thilo Meyer‐Brandis 《Mathematical Finance》2019,29(1):329-367
We specify a general methodological framework for systemic risk measures via multidimensional acceptance sets and aggregation functions. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario‐dependent allocation). We also provide conditions that ensure monotonicity, convexity, or quasi‐convexity of our systemic risk measures. 相似文献
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We propose a generalization of the classical notion of the V@Rλ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance sets. The V@Rλ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on . 相似文献
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We consider an incomplete stochastic financial market where the price processes are described by a vector valued semimartingale
that is possibly non locally bounded. We face the classical problem of utility maximization from terminal wealth, under the
assumption that the utility function is finite-valued and smooth on the entire real line and satisfies reasonable asymptotic
elasticity. In this general setting, it was shown in Biagini and Frittelli (Financ. Stoch. 9, 493–517, 2005) that the optimal
claim admits an integral representation as soon as the minimax σ-martingale measure is equivalent to the reference probability
measure. We show that the optimal wealth process is in fact a supermartingale with respect to every σ-martingale measure with
finite generalized entropy, thus extending the analogous result proved by Schachermayer (Financ. Stoch. 4, 433–457, 2003)
for the locally bounded case.
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Biagini Francesca Fouque Jean-Pierre Frittelli Marco Meyer-Brandis Thilo 《Finance and Stochastics》2020,24(2):513-564
Finance and Stochastics - In our previous paper “A unified approach to systemic risk measures via acceptance sets” (Mathematical Finance, 2018), we have introduced a general class of... 相似文献
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RISK MEASURES AND CAPITAL REQUIREMENTS FOR PROCESSES 总被引:1,自引:0,他引:1
In this paper we propose a generalization of the concepts of convex and coherent risk measures to a multiperiod setting, in which payoffs are spread over different dates. To this end, a careful examination of the axiom of translation invariance and the related concept of capital requirement in the one-period model is performed. These two issues are then suitably extended to the multiperiod case, in a way that makes their operative financial meaning clear. A characterization in terms of expected values is derived for this class of risk measures and some examples are presented. 相似文献