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Motivated by the observation
that the gain-loss criterion, while offering economically meaningful prices of contingent claims,
is sensitive to the reference measure governing the underlying stock price process (a situation
referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure.
Using a dual representation property of polyhedral risk measures
we obtain a one-step, gain-loss criterion based theorem of
asset pricing under ambiguity of...
We consider the following combinatorial game: two players, Fast and Slow, claim k-element subsets of [n] = 1, 2, …, n alternately, one at each turn, so that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed k-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone...
We study ensembles of similar systems
under load of environmental factors. The phenomenon of adaptation
has similar properties for systems of different nature. Typically,
when the load increases above some threshold, then the adapting
systems become more different (variance increases), but the
correlation increases too. If the stress continues to increase
then the second threshold appears: the correlation achieves
maximal value, and start to decrease, but the variance continue to
increase. In many...
We introduce an analog to the notion of Polish space for spaces of weight ≤ κ, where κ is an uncountable regular cardinal such that . Specifically, we consider spaces in which player II has a winning strategy in a variant of the strong Choquet game which runs for κ many rounds. After discussing the basic theory of these games and spaces, we prove that there is a surjectively universal such space and that there are exactly many such spaces up to homeomorphism. We also establish a Kuratowski-like...
In the paper we give a mathematical overview of the CreditRisk+ model as a tool used for calculating credit risk in a portfolio of debts and suggest some other applications of the same method of analysis.
The aim of this paper is to set different lower bounds on the change of the expected net cash flow value at time H > 0 in general term structure models, referring to the studies of Fong and Vasiček (1984), Nawalkha and Chambers (1996), and Balbás and Ibáñez (1998) among others. New immunization strategies are derived with new risk measures: generalized duration and generalized M-absolute of Nawalkha and Chambers, and exponential risk measure. Furthermore, examples of specific one-factor HJM models...
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