The importance and difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. Specifically we focus on expected value type valuations which are based upon the transformation of a fuz...

This is a quantitative study of the valuation and hedging of dangerous options, options whose hedging strategies require unreasonable or risky short positions of the underlying instrument. We examine the valuation of many exotic options, when a shortselling constraint is imposed, as an example for Contingent Claims in Incomplete Markets. The valuation problem is known to be a stochastic control...

The notion of pseudo-valuations (valuations) on a BCC-algebra is introduced by using the Buşneag’s model ([1–3]), and a pseudo-metric is induced by a pseudo-valuation on BCC-algebras. Conditions for a real-valued function to be an BCK-pseudo-valuation are provided. The fact that the binary operation in BCC-algebras is uniformly continuous is provided based on the notion of (pseudo) valuation.

We propose a new theory of IPO underpricing where the asymmetry of the underwriter’s incentives and presence of valuation uncertainty makes underpricing unavoidable. We show how the size of underpricing is defined by valuation uncertainty of the stock (“volatility”) and by the fee level. We quantify the relationship between level of underpricing and level of price volatility. We also show that ...

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Based on the Buşneag’s model ([2, 3, 4]), the notion of pseudovaluations (valuations) on a BE-algebra is introduced, and a pseudometric is induced by a pseudo-valuation on BE-algebras. Related properties are investigated, and conditions for a real-valued function on a BE-algebra to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation in ...

Probability distortions for constructing nonlinear G-expectations for the bid and ask or lower and upper prices in continuous time are here extended to the direct use of measure distortions. Fairly generally measure distortions can be constructed as probability distortions applied to an exponential distribution function on the half line. The valuation methodologies are extended beyond contract ...