Current Topics in Quantitative Finance by Jozsef Abaffy, Marida Bertocchi, Jitka Dupačová (auth.),

By Jozsef Abaffy, Marida Bertocchi, Jitka Dupačová (auth.), Prof. Elio Canestrelli (eds.)

The current quantity collects a variety of revised papers that have been awarded on the twenty first Euro operating team on monetary Modelling assembly, held in Venice (Italy), on October 29-31, 1997. The operating workforce used to be based in September 1986 in Lisbon with the target of delivering a global discussion board for the alternate of knowledge and event; encouraging learn and interplay be­ tween monetary monetary thought and perform of economic choice mak­ ing, in addition to circulating details between universities and monetary associations all through Europe. The attendance to the assembly was once huge and hugely certified. greater than eighty members, coming from 20 diverse nations debated on five invited lectures and forty communications in standard classes. The periods have been positioned on the Island of San Servolo, at the Venetian lagoon, simply in entrance of the Doges Palace. San Servolo Island is a usual oasis, in the middle of a different city atmosphere, supplying nice leisure in a relaxed park and a wide ranging view of Venice. The pleasant surroundings further nice profit to the formal and casual discussions one of the individuals, -which is regular of E.W.G.F.M. conferences. it really is attention-grabbing to contemplate the tale of the assembly. the former destinations have been held at Cyprus, Crete and Dubrovnik - former mile­ stones of the Venitian Republic impact at the Mediterranean Sea. as a result, that this assembly will be harboured within the middle of the Republic itself (namely, the Saint Mark basin), was once just a topic of consequence.

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The introduction of stable distributions bring about a problem with Markowitz' mean-variance rule: stable distributions have infinite variance (and, for certain values of the stability index, have infinite mean) and hence variance and covariance can not be used as decision parameters. Several authors studied portfolio selection problems coping with the lack of variance. Among these, Bawa et al. [1], Fama [5], Press [14], Samuelson [15] and Ziemba [18]. Basically, all these models replace variance with dispersion as a measure of risk and introduce suitable hypotheses on the dependence structure to take the model analytically tractable.

1, Al ~ E~=I V(k). From V(k) ~ V, with k = 1, ... 2, Adn ~ V ~ V(k)/ A 3, with k = 1, ... ,n, that is Adn ~ V(k)A3' Recalling that n = T / h, the lower bound hAIA3 T ~ V(k), k = 1, ... ,n. 2, A3V ~ V(k), with k = 1, ... , n. 1, nA3V ~ E~=I V(k) ~ A 2, that is V ~ A2/(nA3)' Again from V(k) ~ V, with k = 1, ... , n, and again recalling that n = T /h, the upper bound hA2 V(k) ~ TA3' k = 1, ... 3) DenoteL:= (AIA3)/(Tcr) and U := A 2/(TcrA 3). By construction, because Al > 0, A3 > 0 and T > 0, and by hypothesis, because cr E [(A I A 3)/T, A2/(TA 3)] , 0 < L ~ 1 and U ~ 1.

76-77]. When a = 2, a unique representation of the characteristic function can be given by means the covariance matrix: f(O) = exp (i01m - ~OlCO) with t E ]Rn. In the example shown before, we have What we have said for a two-dimensional Normal random vector can be easily extended to n-dimensional vectors [3]. In this context, we will call portfolio any linear combination of assets. Since the returns distribution is assumed to be truly n-dimensional, then any portfolio can be uniquely represented by the coefficients Portfolio Analysis with Symmetric Stable Paretian Returns 53 of the linear combination.

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