57 research outputs found
An efficient segmentation method to price American Put options
A segmentation strategy to price different groups of American standard Put options with different methods is presented and discussed. The method, which exploits the properties of the odd waves of the BI adjusted evaluations introduced by Gaudenzi and Pressacco, proves to be very efficient in particular, to price critical in the money options.American put plain vanilla options; tree evaluation methods; American quality; segmentation
K-Fibonacci sequences and minimal winning quota in Parsimonious game
Parsimonious games are a subset of constant sum homogeneous weighted majority
games unequivocally described by their free type representation vector. We show
that the minimal winning quota of parsimonious games satisfies a second order,
linear, homogeneous, finite difference equation with nonconstant coefficients
except for uniform games. We provide the solution of such an equation which may
be thought as the generalized version of the polynomial expansion of a proper
k-Fibonacci sequence. In addition we show that the minimal winning quota is a
symmetric function of the representation vector; exploiting this property it is
straightforward to prove that twin Parsimonious games, i.e. a couple of games
whose free type representations are each other symmetric, share the same
minimal winning quota
Bilateral symmetry and modified Pascal triangles in Parsimonious games
We discuss the prominent role played by bilateral symmetry and modified
Pascal triangles in self twin games, a subset of constant sum homogeneous
weighted majority games. We show that bilateral symmetry of the free
representations unequivocally identifies and characterizes this class of games
and that modified Pascal triangles describe their cardinality for combinations
of m and k, respectively linked through linear transforms to the key parameters
n, number of players and h, number of types in the game. Besides, we derive the
whole set of self twin games in the form of a genealogical tree obtained
through a simple constructive procedure in which each game of a generation,
corresponding to a given value of m, is able to give birth to one child or two
children (depending on the parity of m), self twin games of the next
generation. The breeding rules are, given the parity of m, invariant through
generations and quite simple.Comment: pp. 2
Twin relationships in Parsimonious Games: some results
In a vintage paper concerning Parsimonious games, a subset of constant sum
homogeneous weighted majority games, Isbell introduced a twin relationship
based on transposition properties of the incidence matrices upon minimal
winning coalitions of such games. A careful investigation of such properties
allowed the discovery of some results on twin games presented in this paper. In
detail we show that a) twin games have the same minimal winning quota and b)
each Parsimonious game admits a unique balanced lottery on minimal winning
coalitions, whose probabilities are given by the individual weights of its twin
game
Bruno de Finetti forerunner of modern finance
In this paper we discuss the role of de Finetti as a forerunner of some
of the more relevant concepts and tools of the modern theory of finance. It is shown
that de Finetti gave some ground breaking contributions in such fields as arbitrage
free pricing, mean variance efficiency, expected utility and risk aversion. We think
it is not only a matter of historical remarks: indeed some of his ideas reveal to be
fruitful even nowadays so that going on studying de Finetti’s papers may be a good
investment for those interested in quantitative finance and economics of uncertainty
Reward-risk efficiency in proportional reinsurance with different risk measures
We have studied, in particular under normality of the implied random variables, the connections between different measures of risk such as the standard deviation, the W-ruin probability and the p-V@R. We discuss conditions granting the equivalence of these measures with respect to risk preference relations and the equivalence of dominance and efficiency of risk-reward criteria involving these measures. Then more specifically we applied these concepts to rigorously face the problem of finding the efficient set of de Finetti’s variable quota share proportional reinsurance
Proper strong-Fibonacci games
We define proper strong-Fibonacci (PSF) games as the subset of proper homogeneous
weighted majority games which admit a Fibonacci representation. This is a
homogeneous, type-preserving representation whose ordered sequence of type weights
and winning quota is the initial string of Fibonacci numbers of the one-step delayed
Fibonacci sequence.We show that for a PSF game, the Fibonacci representation coincides
with the natural representation of the game. A characterization of PSF games
is given in terms of their profile. This opens the way up to a straightforward formula
which gives the number \u3a8(t) of such games as a function of t, number of non-dummy
players\u2019 types. It turns out that the growth rate of \u3a8(t) is exponential. The main
result of our paper is that, for two consecutive t values of the same parity, the ratio
\u3a8(t + 2)/\u3a8 (t) converges toward the golden ratio \u3a6
De Finetti and Markowitz mean variance approach to reinsurance and portfolio selection problems: a comparison
Based on a critical analysis of de Finetti's paper, where the mean variance approach in finance was early introduced to deal with a reinsurance problem, we offer an alternative interpretative key of such an approach to the standard portfolio selection one. We discuss analogies and differences between de Finetti's and Markowitz's geometrical approaches
Sull'anatocismo nell'ammortamento progressivo: un'impostazione non convenzionale
In this paper we analyze, from a logical-mathematical point of view, the problem of the existence of interests on interests (so-called anatocism) in traditional amortization plans for a debt.The elementary methods of repayment of a debt (Bullet Bond and Zero Coupon Bond) are analyzed. It is noted that in them there is respectively absence (BB) or presence (ZCB) of interest on interest. We introduce the decomposition of a debt as a sequence of debts repayable with the two elementary methods. Equivalent decompositions are defined, in one or the other modality, those that give rise to a consolidated amortization that coincides with the traditional amortization plan. An apparent paradox emerges: there would be the presence of interest on interest in the equivalent decomposition ZCB and absence in the equivalent decomposition BB. The paradox can be solved by considering the mathematical consequences of the cadence of the collectability of interest.Keywords: ammortamento progressivo, anatocismo, bullet bond, zero coupon bond. In questo lavoro si analizza, da un punto di vista logico-matematico, il problema dell'esistenza di interessi su interessi (cosiddetto anatocismo) in piani di ammortamento tradizionale di un debito.Dopo aver analizzato le modalità elementari di rimborso di un debito (Bullet Bond e Zero Coupon Bond) e constatato che in esse vi è assenza (BB) o presenza (ZCB) di interessi su interessi, si valutano le conseguenze della scomposizione di un debito in una sequenza di debiti rimborsabili con le due modalità elementari e si definiscono rigorosamente scomposizioni equivalenti, nell'una o nell'altra modalità , quelle che danno vita ad un ammortamento consolidato che coincide con un piano di ammortamento tradizionale. Ne emerge un paradosso apparente: vi sarebbe presenza di interessi nella scomposizione equivalente ZCB e assenza nella scomposizione equivalente BB. Il paradosso si può risolvere considerando le conseguenze matematiche della cadenza dell'esigibilità degli interessi
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