ISSN:
1432-1122
Keywords:
Key words:Dynamic measures of risk, Bayesian risk, hedging, capital requirements, value-at-risk
;
JEL classification: G11, G13, C73
;
Mathematics Subject Classification (1991):90A09, 90A46, 93E20, 60H30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract. In the context of complete financial markets, we study dynamic measures of the form \[ \rho(x;C):=\sup_{\nu\in\D} \inf_{\pi(\cdot)\in\A(x)}{\bf E}_\nu\left(\frac{C-X^{x, \pi}(T)}{S_0(T)}\right)^+, \] for the risk associated with hedging a given liability C at time t = T. Here x is the initial capital available at time t = 0, ${\cal A}(x)$ the class of admissible portfolio strategies, $S_0(\cdot)$ the price of the risk-free instrument in the market, ${\cal P}=\{{\bf P}_\nu\}_{\nu\in{\cal D}}$ a suitable family of probability measures, and [0,T] the temporal horizon during which all economic activity takes place. The classes ${\cal A}(x)$ and ${\cal D}$ are general enough to incorporate capital requirements, and uncertainty about the actual values of stock-appreciation rates, respectively. For this latter purpose we discuss, in addition to the above “max-min” approach, a related measure of risk in a “Bayesian” framework. Risk-measures of this type were introduced by Artzner, Delbaen, Eber and Heath in a static setting, and were shown to possess certain desirable “coherence” properties.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s007800050071
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