the perturbed compound poisson risk model with two sided jumps in this paper we consider a perturbed compound poisson risk model with two sided jumps the downward jumps represent the claims following an arbitrary distribution while the upward jumps are also allowed to represent the random gains assuming that the density function of the upward jumps has a rational laplace transform the laplace transforms and defective renewal equations for the discounted penalty functions are derived and the asymptotic estimate for the probability of ruin is also studied for heavy tailed downward jumps finally some explicit expressions for the discounted penalty functions as well as numerical examples are given

a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

dynamic feedback over commutative rings abstract we call a commutative ring r a ca n ring if for each n dimensional reachable system f g over r the system augmented by rank n projective modules with f augmented by a zero map and g augmented by an identity map is coefficient assignable we show that if r is a dedekind domain then r is a ca n 1 ring in particular a principal ideal domain is a ca n 1 ring we also show that if r is a ring with the gcs property and the 2 generator property then r is a ca 2 n 2 ring

partitions of elements in a monoid and its applications to systems theory abstract the feedback class of a locally brunovsky linear system is fully determined by the decomposition of state space as direct sum of system invariants 2 in this paper we attack the problem of enumerating all feedback classes of locally brunovsky systems over an n dimensional state space and translate to the combinatorial problem of enumerating all the partitions of integer n in some abelian semigroup the problem of computing the number n k of all the partitions of integer n into k different summands is pointed out

occupation times of hyper exponential jump diffusion processes with application to price step options we are interested in occupation times of jump diffusion processes with hyper exponentially distributed jump sizes we develop a new approach to derive analytical formulas for the laplace transform of the joint distribution of a hyper exponential jump diffusion process and its occupation times these formulas are then used to price step options

on feedback invariants for linear dynamical systems abstract the goal of this paper is to prove that if r is a commutative ring containing a non zero finitely generated maximal ideal m containing its annihilator such that every unit of r m lifts to a unit of r then the category of reachable systems over r is wild in the sense of classical representation theory from this it follows that a canonical form for a reachable system over a pid is not likely to be found more specifically canonical forms are unlikely to be found for systems over z and k t when k is a field

exit problems for jump processes with applications to dividend problems this paper investigates the first passage times to flat boundaries for hyper exponential jump diffusion processes explicit solutions of the laplace transforms of the distribution of the first passage times the joint distribution of the first passage times and undershoot overshoot the joint distribution of the process and running suprema infima are obtained the processes recover many models appearing in the literature such as the compound poisson risk models the diffusion perturbed compound poisson risk models and their dual models as applications we present explicit expressions of the dividend formulae for barrier strategy and threshold strategy

enumeration of classes of linear systems via equations and via partitions in an ordered abelian monoid abstract we prove that the feedback classes of locally brunovsky linear systems are given by the decomposition of state space into direct summands hence the problem of enumerating feedback classes of systems is equivalent to the problem of enumerating all solutions of a linear equation over a commutative zerosumfree monoid if this monoid is also cancelative then the problem is solved by all the partitions

coefficient assignability and a block decomposition for systems over rings abstract we characterize the class of commutative rings r such that for any linear system a b with coefficients in r one can extract the reachable part of the system in a way similar to the classical kalman controllability decomposition for systems over fields the notion of strong ca ring is introduced as the class of commutative rings over which any system verifies a strong form of the coefficient assignability property it is shown that the class of strong ca rings lies strictly between the classes of rings with strong versions of the known pole assignability pa and feedback cyclization fc properties defined only for reachable systems we prove that for ucu rings for example polynomials with coefficients in a field the usual pa ca and fc properties are equivalent to the corresponding strong forms of these properties in particular c y is a strong ca ring

canonical forms for single input linear systems in this paper we obtain a canonical form for single input n dimensional linear systems over z and in general over a bezout domain we also give an algorithm to obtain that canonical form

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

knorr lattices their characters and some subsets of fpd examples of positive height cyclic knorr lattices for elementary abelian p groups are constructed and bounds relating the height of such lattices to the size of the group are given the problem is formulated in terms of finite geometry when p 2 certain examples are shown to arise from difference sets

g algebras clifford theory and the green correspondence let g be a finite group with subgroup h loosely speaking clifford theory as developed by e c dade and others is a tool for constructing reduction arguments in the case where h is normal in g the green correspondence is a tool for constructing reduction arguments in the case where h contains the normaliser in g of a given p subgroup or more generally where h contains the normaliser of a given local pointed group here we cover both of these situations by considering the case where no h contains the normaliser in g of a given local pointed group a brief discussion in 1 indicates how puig s theory subsumes the green correspondence and aspects of clifford theory here this theme is given a more systematic treatment we shall see in particular that defect pointed subgroups the green correspondence and brauer s extended first main theorem are all manifestations of a more general mechanism let be a complete local commutative noetherian ring with an algebraically closed residue field k of prime characteristic p throughout we fix a g algebra a all algebras are deemed to possess a unity element all algebras and modules are to be free over or over k and of finite rank for the rest of this section let us fix points 3 a of h g respectively on a and suppose that ht3 g have a common defect pointed subgroup pr such that nc p ng h it is easy to show see section 4 t h a t if p is another defect pointed subgroup of ht3 then p is also a defect pointed subgroup of g and ng p ng h it t ranspires again see section 4 t h a t ht3 g if and only if a c trgh ah 3ah when these equivalent

numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric levy motion abstract for non gaussian stochastic dynamical systems mean exit time and escape probability are important deterministic quantities which can be obtained from integro differential nonlocal equations we develop an efficient and convergent numerical method for the mean first exit time and escape probability for stochastic systems with an asymmetric levy motion and analyze the properties of the solutions of the nonlocal equations the discretized equation has toeplitz structure that enables utilization of fast fourier transform in numerical simulations we also investigate the effects of different system factors on the mean exit time and escape probability including the skewness parameter the size of the domain the drift term and the intensity of gaussian and non gaussian noises we find that the behavior of the mean exit time and the escape probability has dramatic difference at the boundary of the domain when the index of stability crosses the critical value of one

elementary construction of the quiver of the mackey algebra for groups with cyclic normal p sylow subgroup through recent investigations of j thrvenaz and p j webb 4 8 the concept of mackey functors being originally introduced by j a green 3 and studied by a w m dress t yoshida h sasaki and others has regained considerable interest an important reason for this is i new interpretation of a conjecture of aiperin in terms of mackey functors in 8 using results of 7 given a commutative ring 4 by its definition it is immediate that the category of mackey functors over 4 for a finite group g is an abelian category even that it is the category of 4 representations of a quiver with relations 8 namely a mackey functor for g associates to each subgroup of g a module and moreover certain linear maps between these spaces satisfying certain relations involving g thus a mackey functor for g can be interpreted as a module over a path algebra of a quiver with relations the so called mackey algebra 6 9 the main difference to the usual representation theory of quivers and thus the main problem of interpreting mackey functors as such representations lies in the fact that the maps between these spaces do not lie in the radical of this path algebra and this path algebra is not basic in general so it is a natural problem to compute the quiver in the usual sense for the category of mackey functors for a group g in particular in the case where 4 is a field of characteristic p dividing the order of g the question of when there are up to isomorphism only finitely many indecomposable mackey functors for g led to recent investigations of thrvenaz and webb solving this problem in general and it also led to the investigations we present in this paper which presents in a special situation namely if g has a normal cyclic p sylow subgroup an explicit computation of the quiver of the now so called mackcy algebra by definition the mackey algebra is the basic algebra whose category of finitely generated

the pointwise feedback relation for linear dynamical systems abstract let and be two m input n dimensional linear dynamical systems over a commutative ring r if is feedback equivalent to then is pointwise feedback equivalent to i e for all prime ideal p of r the systems p and p are feedback equivalent over the residue field k p where p is the natural extension of to k p this paper is devoted to the study of the pointwise feedback relation we characterize when two systems and are pointwise equivalent we show that r is an absolutely flat ring if and only if the feedback relation and the pointwise feedback relation are equivalent the particular case of rings of real valued continuous functions is specially treated

option pricing under a double exponential jump diffusion model this paper aims to extend the analytical tractability of the black scholes model to alternative models with arbitrary jump size distributions more precisely we propose a jump diffusion model for asset prices whose jump sizes have a mixed exponential distribution which is a weighted average of exponential distributions but with possibly negative weights the new model extends existing models such as hyperexponential and double exponential jump diffusion models because the mixed exponential distribution can approximate any distribution as closely as possible including the normal distribution and various heavy tailed distributions the mixed exponential jump diffusion model can lead to analytical solutions for laplace transforms of prices and sensitivity parameters for path dependent options such as lookback and barrier options the laplace transforms can be inverted via the euler inversion algorithm numerical experiments indicate that the formulae are easy to implement and accurate the analytical solutions are made possible mainly because we solve a high order integro differential equation explicitly a calibration example for spy options shows that the model can provide a reasonable fit even for options with very short maturity such as one day this paper was accepted by michael fu stochastic models and simulation

the effective calculation of all assignable polynomials to a single input system over a bezout domain the set of all feedback assignable polynomials to a given single input system over a bezout domain is obtained the general case is reduced to the case of weakly reachable systems for these systems a canonical form for the algebraic equivalence is obtained algorithms and examples over a euclidean domain and in particular over the ring z of rational integers are also given the problem of deciding and feedback assignment of a given polynomial to a given non reachable n dimensional linear system is solved effectively up to a cost of o n4 arithmetic operations

on matrix inverses modulo a subspace given a pair of matrices a b rn n rn m with coefficients in a commutative ring we study the problem of finding a matrix f such that a bf becomes invertible we point out some relations between the problem of finding feedback inverses of a modulo b and the pole shifting problem for the pair a b in fact we give feedback invertibility results over a well known large class of rings related with the pole shifting the class of pa rings on the other hand we also give a pointwise global characterization the ring r of rational integers and the coordinate ring of the real unit circle r x y x2 y2 1 are studied in some detail finally the problem of derivative feedback standardization of generalized linear systems is reviewed as a particular case

on the duality principle for linear dynamical systems over commutative rings abstract the main result in this paper characterizes those commutative rings r having the property that every linear dynamical system over r verifies the duality principle i e the system is observable reachable if and only if the dual system t is reachable observable this characterization is given in terms of the finitely generated faithful ideals of r and it generalizes a result due to ching and wyman for the noetherian case in case r satisfies the additional condition of being a reduced ring we prove that the duality principle holds in r if and only if the height of every finitely generated ideal of r is zero

feedback invariants for linear dynamical systems over a principal ideal domain abstract this paper studies the action of the feedback group f n m on m input n dimensional reachable linear dynamical systems over a principal ideal domain r for such a 2 dimensional system a complete set of invariants is given which characterizes the feedback class of in particular it is characterized in terms of these invariants when has the feedback cyclization property the particular cases r z and r r x are studied in some detail finally when n is arbitrary the feedback classification is given for the class of reachable systems f g such that g is a matrix with at least n 1 invariant factors equal to one

duality in g algebras keywords finite group complete discrete valuation ring symmetric g algebra symmetric bilinear form projective ideal symmetric algebra rg lattice unimodular symmetric g algebra almost projective ideal almost split sequences block defect groups virtually irreducible lattices splitting trace lattices reference ctg article 1988 005doi 10 1007 bf01161746 record created on 2008 12 16 modified on 2017 05 12

the dade group of mackey functors for p groups abstract we introduce endo permutation mackey functors and the mackey dade group of a p group and study their basic properties we exhibit relations between the mackey dade group of a finite p group p and the dade groups of the weyl groups of all subgroups of p as a result we show that the mackey dade group tensored with q over z is the kernel of the linearization map for mackey functors introduced by the author

occupation times of jump diffusion processes with double exponential jumps and the pricing of options in this paper we provide laplace transform based analytical solutions to pricing problems of various occupation time related derivatives such as step options corridor options and quantile options under kou s double exponential jump diffusion model these transforms can be inverted numerically via the euler laplace inversion algorithm and the numerical results illustrate that our pricing methods are accurate and efficient the analytical solutions can be obtained primarily because we derive the closed form laplace transform of the joint distribution of the occupation time and the terminal value of the double exponential jump diffusion process beyond financial applications the mathematical results about occupation times of a jump diffusion process are of more general interest in applied probability

pricing exotic derivatives exploiting structure in this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring occurs and the underlying evolves according to a markov one dimensional stochastic processes the approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed up of the recursion the algorithm is general and is examined in detail with reference to the cev constant elasticity of variance process for pricing different exotic derivatives such as asian barrier bermudan lookback and step options for which up to date no efficient procedures are available extensive numerical experiments confirm the theoretical results the matlab code used to perform the computation is available online at http www1 mate polimi it marazzina bp htm 2013 elsevier b v all rights reserved

on the k theory of feedback actions on linear systems abstract a categorical approach to linear control systems is introduced feedback actions on linear control systems arise as symmetric monodical category s r stable feedback isomorphisms generalize dynamic enlargement of pairs of matrices subcategory of locally brunovsky linear systems b r is studied we prove that the stable feedback isomorphisms of locally brunovsky linear systems are characterized by the grothendieck group k 0 b r hence a link from linear dynamical systems to algebraic k theory is established

anchors of irreducible characters given a prime number p every irreducible character of a finite group g determines a unique conjugacy class of p subgroups of g which we will call the anchors of this invariant has been considered by barker in the context of finite p solvable groups besides proving some basic properties of these anchors we investigate the relation to other p groups which can be attached to irreducible characters such as defect groups vertices in the sense of j a green and vertices in the sense of g navarro

strong feedback cyclization for systems over rings abstract for nonnecessarily reachable systems over a commutative ring r we define a strong form of feedback cyclization fc with this natural generalization of the fc property we obtain a feedback reduced form for systems over strong fc rings i e rings for which every system verifies the fc property in the particular case of reachable single input systems this gives the usual control canonical form of bumby et al remarks on the pole shifting problem over rings j pure appl algebra 20 1981 113 127 also it is proved that a commutative ring with 1 in its stable range has the strong fc property if and only if it has the ucu property which is the natural parallel form of the result given by brewer et al pole assignability in polynomial rings power series rings and prufer domains j algebra 106 1987 265 286 for the reachable case many classes of rings which were known to be fc rings are in fact strong fc rings but there are fc rings which are not strong fc rings

the parametrization of interior algebras keywords finite group indecomposable og lattice invariants vertex source multiplicity module indecomposable projective lattice twisted group algebra primitive interior g algebras reference epfl article 130446doi 10 1007 bf02571667 record created on 2008 12 16 modified on 2017 05 12

a characterization of gcu rings with the fc2 property abstract we study linear systems f g with coefficients in a commutative ring r with the gcu property whenever f g is controllable there exists a vector u with gu unimodular our main result is a gcu ring is an fc2 ring i e every two dimensional controllable system over r is feedback cyclizable if and only if r satisfies the following property for any finitely generated ideal i and f invertible modulo i there exist a unit u and an element h with f uh2 mod i

iterative algorithm for the first passage time distribution in a jump diffusion model with regime switching and its applications for a regime switching model with a finite number of regimes and double phase type jumps jiang and pistorius 2008 derived matrix equations with real parameters for the wiener hopf factorization the laplace transform of the first passage time distribution is expressed in terms of the solution of the matrix equations in this paper we provide an iterative algorithm for solving the matrix equations of jiang and pistorius 2008 with complex parameters this makes it possible to obtain numeric values of the laplace transform with complex parameters for the first passage time distribution the laplace transform with complex parameters can be inverted by numerical inversion algorithms such as the euler method as an application we compute the prices of defaultable bonds under a structural model with regime switching and double phase type jumps

a characterization of von neumann rings in terms of linear systems abstract a new characterization of commutative von neumann regular rings is given in terms of linear control systems having locally a brunovsky canonical form the problem of enumerating reachable systems over certain von neumann regular ring is solved extending classical results over fields

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

when are dynamic and static feedback equivalent an open question in control theory over commutative rings is when does dynamic feedback equivalence imply static feedback equivalence a second open problem is given a linear system a b when does there exist a matrix f such that a bf is invertible in this paper we solve both questions obtaining two characterizations of stable rings

default probability of american lookback option in a mixed jump diffusion model abstract this paper considers the default probability of american lookback option in a mixed jump diffusion model where the underlying asset price has to cross two sided predetermined strikes to activate the american lookback option we study a default problem with the bankruptcy time being defined as the first passage time of the underlying asset price by solving a system of coupled mjd fbm we obtain an explicit formula for the laplace transform of the default time some numerical results are given for illustration

comments on pole assignability over rings abstract we observe that the proof by eising of the pole assignment theorem for linear systems over a principal ideal domain 4 actually remains valid for any elementary divisor ring for large classes of rings matrix characterizations of pole assignability are given

dynamic feedback over principal ideal domains and quotient rings let r be a principal ideal domain in this paper we prove that for a large class of linear systems dynamic feedback over r is equivalent to static feedback over a quotient ring of r in particular when r is the ring of integers z one has that the static feedback classification problem over finite rings is equivalent to the dynamic feedback classification problem over z restricted to a special type of system

feedback classification of linear systems over von neumann regular rings abstract it is proved that feedback classification of a linear system over a commutative von neumann regular ring r can be reduced to the classification of a finite family of systems each of which is properly split into a reachable and a non reachable part where the reachable part is in a brunovski type canonical form while the non reachable part can only be altered by similarity if a canonical form is known for similarity of matrices over r then it can be used to construct a canonical form for feedback equivalence an explicit algorithm is given to obtain the canonical form in a computable context together with an example over a finite ring

the dynamic feedback equivalence over principal ideal domains we show that over a principal ideal domain the dynamic feedback equivalence for not necessarily reachable linear systems is reduced to the feedback equivalence for one augmented systems we also obtain the dynamic feedback classification for two dimensional linear systems

categorifying induction formulae via divergent series abstract we show how to get explicit induction formulae for finite group representations and more generally for rational green functors by summing a divergent series over dwyer s subgroup and centralizer decomposition spaces this results in formulae with rational coefficients the former space yields a well known induction formula the latter yields a new one as essentially immediate corollaries of the existing literature we get similar formulae in group cohomology and stable splittings of classifying spaces

estimating the gerber shiu function in the perturbed compound poisson model by laguerre series expansion abstract in this paper we study the statistical estimation of the gerber shiu function in the compound poisson risk model perturbed by diffusion this problem has been solved in 32 by the fourier sinc series expansion method different from 32 we use the laguerre series to expand the gerber shiu function and propose a relevant estimator the estimator is easily computed and has fast convergence rate various simulation studies are presented to confirm that the estimator performs well when the sample size is finite

statistical properties and economic implications of jump diffusion processes with shot noise effects abstract the shot noise jump diffusion snjd model aims to reflect how economic variables respond to the arrival of sudden information this paper analyzes the snjd model providing its statistical distribution and closed form expressions for the characteristic function and moments we also analyze the dynamics of the model concluding that the degree of serial autocorrelation is related to the occurrence and magnitude of abnormal information in addition we provide some useful approximations in a particular case that considers exponential type decay empirically we propose a gmm approach to estimate the parameters of the model and present an empirical application for the stocks included in the dow jones averaged index our findings seem to confirm the presence of shot noise effects in 73 of the stocks and a strong relationship between the shot noise process and the autocorrelation pattern embedded in data

brunovsky s canonical form for linear dynamical systems over commutative rings abstract this paper is devoted to studying the action of the feedback group on linear dynamical systems over a commutative ring r with unit we characterize the class of m input n dimensional reachable linear dynamical systems f g over r that are feedback equivalent to a system c fc gc with brunovsky s canonical form this characterization is obtained in terms of the minors of the matrices g i g fg f i 1 g for 1 i n

g algebras jacobson radical and almost split sequences keywords finite group indecomposable kg module sas sequence almost split exact sequences restriction relative jacobson radicals local criterion multiplicity module vertex source indecomposable projective module twisted group algebra induction reference ctg article 1988 006doi 10 1007 bf01393690 record created on 2008 12 16 modified on 2017 05 12

regulation of split linear systems over rings coefficient assignment and observers a theory of regulators is developed for finite free split linear systems over a commutative ring k this is achieved by developing a theory of coefficient assignment and observers it is shown that the problem of coefficient assignment can be solved for reachable systems by using dynamic state feedback for strongly observable systems it is shown that observers with arbitrary dynamics can be constructed internal stability of observer and state feedback configuration is considered explicitly some examples are given to illustrate these techniques

brownian excursion the m m 1 queue and their occupation times the one and two dimensional distributions of the occupation time and of the local time of brownian excursion are derived these results follow from a suitable conditioned weak limit theorem more specifically we shall prove that the normalized virtual waiting time process of the m m 1 queue conditioned by the length of its first busy period weakly converges to the brownian excursion process at the end of this paper we shall discuss the connection between the local time of the brownian excursion process and the number of downcrossings during the first busy period of an m g 1 queue this connection seems to be very interesting for the theory of branching processes