We introduce an expected utility approach to price insurance risks in a dynamic Ž nancial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices—one each fo...

Weitzman’s Dismal Theorem (Weitzman 2009) challenged the economic analysis of climate policy: The uncertainty about the impact of climate change would be so large that expected utility maximisation is either undefined or arbitrary. Unfortunately, Weitzman’s is an impossibility theorem: It shows what cannot be done. It does not show what could or should be done instead. This paper attempts to pr...

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the “average of the 100p% worst losses” in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes.

In English auctions, introducing a buy price, i.e., the seller’s maximum price bid at which any bidder at any time can immediately win the auction, allows the seller to gain higher expected utility than that in a traditional auction when either the seller or the buyers are risk-averse. If the seller sets the buy price high enough, the buyprice English auction is efficient and guarantees the hig...

In this paper we test several risk management models for computing expected shortfall for one-period hedge errors of hedged derivatives positions. Contrary to value-at-risk, expected shortfall cannot be tested using the standard binomial test, since we need information of the distribution in the tail. As derivatives positions change characteristics and thereby the size of risk exposures over ti...

I develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the Anscombe-Aumann approach to subjective expected utility. I observe that a decision maker is unaware of an event if and only if her choices reveal that the event is “null” and the negation of the event is “null”. Moreover, I...

A considerable number of equivalent formulas defining conditional value-at-risk and expected shortfall are gathered together. Then we present a simple method to bound the conditional value-at-risk of compound Poisson loss distributions under incomplete information about its severity distribution, which is assumed to have a known finite range, mean, and variance. This important class of nonnorma...

As a natural extension of the fuzzy variable, bifuzzy variable is defined as mapping from credibility space to collection variables, which an appropriate tool model two-fold phenomena. In order enrich its theoretical foundation, this paper explores some important measures for regular most commonly used type variables. Firstly, we introduce variables’ mean chance measure and properties, includin...

The earth mover's distance (EMD), also called the first Wasserstein distance, can be naturally extended to compare arbitrarily many probability distributions, rather than only two, on set $[n]=\{1,\dots,n\}$. We present details for this generalization, along with a highly efficient algorithm inspired by combinatorics; it turns out that in special case of three EMD is half sum pairwise EMD's. Ex...