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The paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging strategy is measured by a general risk function. Convex Optimization Theory is used in order to extend pricing rules for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. Necessary and sufficient optimality conditions...
This paper has considered a risk measure ρ and a (maybe incomplete and/or imperfect) arbitrage-free market with pricing rule Π. They are said to be compatible if there are no reachable strategies y such that Π(y) is bounded and ρ(y) is close to −∞. We show that the lack of compatibility leads to meaningless situations in financial or actuarial applications. The presence of compatibility is characterized...
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