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Bayesian risk measures for derivatives via random Esscher transform. (English) Zbl 1083.62544

Summary: This paper proposes a model for measuring risks for derivatives that is easy to implement and satisfies a set of four coherent properties introduced by P. Artzner et al. [Math. Finance 9, 203–228 (1999; Zbl 0980.91042)]. We construct our model within the context of Gerber-Shiu’s option-pricing framework. A new concept, namely Bayesian Esscher scenarios, which extends the concept of generalized scenarios, is introduced via a random Esscher transform. Our risk measure involves the use of the risk-neutral Bayesian Esscher scenario for pricing and a family of real-world Bayesian Esscher scenarios for risk measurement. Closed-form expressions for our risk measure can be obtained in some special cases.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 0980.91042

Software:

RiskMetrics
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References:

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