DYNAMIC RISK MEASURES AND G-EXPECTATION
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A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property dis-couraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which general-ize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.
Abstract
A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property dis-couraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which general-ize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.
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