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

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

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

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

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

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

Camel welfare: survey on camel caretakers' perspectives

Animal welfare depends on caretakers' handling and management skills. The study aimed at gaining information on camel caretakers' backgrounds, their perceptions of welfare and management practices and at investigating associations with camel health and behavioural problems. The study was conducted at a camel market in Qatar and 49 caretakers were interviewed (29 questions). Caretakers were male, mainly from Sudan (91.7%; P<0.001), and had mainly learned camel management from family members (81.6%; P<0.001). Camels were mainly from Qatar, reared for milk, breeding or meat. The majority of the caretakers under 30 years took care of camels reared as breeding animals or for milk production (n=12, 75.0%), while the caretakers over 40 years took care of camels for dual-purposes (n=7, 46.7%; P<0.05) or meat (n=4, 26.7%). Camels received rationed feed and water (87.6%, 53.1%, P<0.001), and were dewormed regularly (96.8%, P<0.001) but not vaccinated (72.9%; P<0.001). Respondents experienced at least one camel with a behavioural (45.8%) and a health (87.8%) problem and associations between management practices and those problems were found. Behavioural problems were associated with the number of health problems, suggesting that sick camels tended to show behavioural modifications. Caretakers ranked their ability to recognise a camel in distress/pain as high, reporting that the first sign was a change in behaviour. The caretakers' understanding of animal welfare was, however, low, missing the overall meaning of the concept; most caretakers defined animal welfare according to only one (52.2%) welfare principle. Overall, early and appropriate treatment of camels with health and behavioural problems, an increased presence of veterinarians at camel farms, and education on camel behaviour and welfare are recommended