explicit solution of a general consumption investment problem this paper solves a general consumption and investment decision problem in closed form an investor seeks to maximize total expected discounted utility of consumption there are n distinct risky investments modelled by dependent geometric brownian motion processes and one riskless deterministic investment the analysis allows for a general utility function and general rates of return the model and analysis take into consideration the inherent nonnegativity of consumption and consider bankruptcy so this paper generalizes many of the results of lehoczky sethi and shreve lehoczky j s sethi s shreva 1983 optimal consumption and investment policies allowing consumption constraints and bankruptcy math oper res 8 613 636 the value function is determined explicitly as are the optimal consumption and investment policies the analysis is extended to consider more general risky investments under certain conditions the value functions derived for geometric brownian motion are shown to provide upper and lower bounds on the value functions in the more general context

on mod p properties of siegel modular forms we prove two results on mod p properties of siegel modular forms first we use theta series in order to construct of a siegel modular form of weight p 1 which is congruent to 1 mod p second we define a theta operator vartheta on q expansions and show that the algebra of siegel modular forms mod p is stable under vartheta by exploiting the relation between vartheta and generalized rankin cohen brackets

on an investment consumption model with transaction costs this paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log normal diffusions we suppose that transactions between the assets incur a cost proportional to the size of the transaction the problem is to maximize the total utility of consumption dynamic programming leads to a variational inequality for the value function existence and uniqueness of a viscosity solution are proved the variational inequality is solved by using a numerical algorithm based on policies iterations and multigrid methods numerical results are displayed for n 1 and n 2

notes on matrices with diagonally dominant properties abstract in this paper we analyze the relation between some classes of matrices with variants of the diagonal dominance property we establish a sufficient condition for a generalized doubly diagonally dominant matrix to be invertible sufficient conditions for a matrix to be strictly generalized diagonally dominant are also presented we provide a sufficient condition for the invertibility of a cyclically diagonally dominant matrix these sufficient conditions do not assume the irreducibility of the matrix

dashnic zusmanovich type matrices a new subclass of nonsingular h matrices abstract a new class of matrices called dashnic zusmanovich type dz type matrices which is similar to but different from dashnic zusmanovich dz matrices is introduced and proved to be a subclass of nonsingular h matrices the relations between strictly diagonally dominant matrices doubly strictly diagonally dominant matrices dz matrices and dz type matrices are discussed finally by the non singularity of dz type matrices a new eigenvalue localization set for matrices is given

an iterative criterion for h matrices we provide an algorithmic characterization of h matrices when a is an h matrix this algorithm determines a positive diagonal matrix d such that ad is strictly row diagonally dominant in effect d is produced iteratively by quantifying and

on iterative criteria for h and non h matrices the identification of the h matrix property of the coefficient matrix of a linear system of equations is of great theoretical and practical importance since h matrices have many applications in science and engineering for this identification many direct and iterative criteria already exist in this article we present new iterative criteria which are proved to be faster than similar previous ones for the desired identification these criteria may also take advantage of a possible sparsity of the matrix together with the algorithms that are proposed various illustrative numerical examples are provided

classes of general h matrices let m a denote the comparison matrix of a square h matrix a that is m a is an m matrix h matrices such that their comparison matrices are nonsingular are well studied in the literature in this paper we study characterizations of h matrices with either singular or nonsingular comparison matrices the spectral radius of the jacobi matrix of m a and the generalized diagonal dominance property are used in the characterizations finally a classification of the set of general h matrices is obtained

note on mod p siegel modular forms ii the structure of the ring of mod p siegel modular forms of degree two is determined in the cases where the prime p is 2 or 3

simple criteria for nonsingular h matrices in this paper several new simple criteria for nonsingular h matrices are obtained by making use of elements of matrices only advantages are illustrated by numerical examples and a necessary condition for nonsingular h matrices is also presented

an optimal investment consumption model with borrowing this paper considers a consumption and investment decision problem for a single agent wealth is divided between a riskless asset and a risky asset with logarithmic brownian motion price fluctuations short selling is not allowed but borrowing is allowed at rate exceeding the rate of return on the riskless asset an explicit solution of the dynamic programming differential equation for the maximum total discounted expected utility function u is available only in the hara case however using viscosity solution methods the asymptotic behavior of the value function v x is found for small wealth x and for large wealth x

stochastic control theory and operational research abstract the paper gives an overview of stochastic optimal control theory and its applications to operational research stochastic control theory deals with the intertemporal optimization of dynamic systems under uncertainty after a short review of deterministic optimal control theory and the theory of stochastic dynamic systems a general stochastic optimal control problem is formulated both in discrete and continuous time among the method for solving such problems particularly stochastic dynamic programming and the stochastic maximum principle are introduced examples from the areas of finance advertising production inventory models and information policy illustrate the applicability of stochastic control theory to operational research problems moreover its actual and potential impact on or is discussed from a methodological point of view

optimization problem for a portfolio with an illiquid asset lie group analysis abstract management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance one of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a portfolio cannot be sold until a certain finite infinite or random moment of time this approach arises a certain amount of models that are actively studied at the moment working in the merton s optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid a risky and a risk free asset our goal in this paper is to carry out a complete lie group analysis of pdes describing value function and investment and consumption strategies for a portfolio with an illiquid asset that is sold in an exogenous random moment of time with a prescribed liquidation time distribution the problem of such type leads to three dimensional nonlinear hamilton jacobi bellman hjb equations such equations are not only tedious for analytical methods but are also quite challenging form a numeric point of view to reduce the three dimensional problem to a two dimensional one or even to an ode one usually uses some substitutions yet the methods used to find such substitutions are rarely discussed by the authors we find the admitted lie algebra for a broad class of liquidation time distributions in cases of hara and log utility functions and formulate corresponding theorems for all these cases we use found lie algebras to obtain reductions of the studied equations several of similar substitutions were used in other papers before whereas others are new to our knowledge this method gives us the possibility to provide a complete set of non equivalent substitutions and reduced equations

the ring of modular forms of degree two in characteristic three we determine the structure of the ring of siegel modular forms of degree 2 in characteristic 3

congruences between siegel modular forms using the moduli theory of abelian varieties and a recent result of bocherer nagaoka on lifting of the generalized hasse invariant we show congruences between the weights of siegel modular forms with congruent fourier expansions this result implies that the weights of p adic siegel modular forms are well defined

group representations and lattices this paper began as an attempt to understand the euclidean lattices that were recently constructed using the theory of elliptic curves by elkies e and shioda shl sh2 from the point of view of group representations the main idea appears in a note of thompson th2 if one makes strong irreducibility hypotheses on a rational representation v of a finite group g then the g stable euclidean lattices in v are severely restricted unfortunately these hypotheses are rarely satisfied when v is absolutely irreducible over q but there are many examples where the ring endg v is an imaginary quadratic field or a definite quaternion algebra these representations allow us to construct some of the mordell weil lattices considered by elkies and shioda as well as some interesting even unimodular lattices that do not seem to come from the theory of elliptic curves in 1 we discuss lattices and hermitian forms on y7 and in 2 4 the strong irreducibility hypotheses we wish to make in 5 we show how our hypotheses imply the existence of a finite number up to isomorphism of euclidean z g lattices l in v with endg l a maximal order in endg v we give some examples with dim v 8 in 6 and in 7 9 discuss the invariants of l such as the dual lattice and theta function the rest of the paper is devoted to examples in most g is a finite group of lie type and v is obtained as an irreducible summand of the weil representation of g some of the representation theoretic problems left open by this paper are to find all examples of pairs g v satisfying the strong irreducibility hypotheses of 2 4 and to determine the invariants shortest nonzero vector theta function thompson series of the g lattices l so effortlessly constructed inside v

new criteria for identifying h matrices in the recent paper of gan and huang linear algebra appl 374 2003 317 several simple criteria as well as a necessary condition for nonsingular h matrices have been obtained inspired by this work we will define several new subclasses of nonsingular h matrices and give necessary conditions for a matrix to be an h matrix finally as a result of numerical experiments we establish relations between defined and some already known subclasses

criterions for the positive definiteness of real supersymmetric tensors the positive definiteness of an even degree homogeneous polynomial form f x plays an important role in the stability study of nonlinear autonomous systems via lyapunov s direct method in automatic control and the positive definiteness of f x is equivalent to that of an even order supersymmetric tensor which defines f x in this paper we provide some criterions for identifying the positive definiteness of an even order real supersymmetric tensor moreover an iterative algorithm for identifying the positive definiteness of an even order real supersymmetric tensor is obtained numerical examples are given to verify the corresponding results

optimal consumption and investment policies allowing consumption constraints and bankruptcy an agent can distribute his wealth between two investments one with a fixed rate of return r and the other with a random rate of return modeled as a diffusion with mean r the agent seeks to maximize total discounted utility from consumption over an infinite horizon consumption may be constrained from below various models for bankruptcy including welfare are considered the agent has a strictly concave utility function for consumption however it is shown that the utility function for wealth may have convex portions thus the agent may be risk seeking the paper gives a complete treatment of the existence and nonexistence of optimal policies new theorems for the optimal control of degenerate diffusions are given as well as explicit formulas for the value function

a note on the convergence of the aor method abstract in gao and huang z x gao t z huang convergence of aor method appl math comput 176 2006 134 140 some practical sufficient conditions for the convergence of the aor accelerated overrelaxation method for solving linear system ax b with a being doubly diagonally dominant matrix are presented using a different approach we will give some improvements in both cases when the matrix a is either strictly diagonally dominant sdd or doubly diagonally dominant using the same simple example as in gao and huang 2006 we will illustrate how the new approach can significantly improve convergence area

application of generalized diagonal dominance in wireless sensor network optimization problems abstract the recent application of the diagonal dominance in the development of the optimization algorithms in the wireless sensor networks design has been done by yuan and yu 2006 14 extended in yu et al 2006 9 and surveyed in machado and tekinay 11 in this paper we will use the concept of generalized diagonal dominance to improve the obtained results regarding the power control game in three directions we also discuss the applicability of such improvements

trace operators and theta series for γ 0 n q and γ n q we consider the action of suitable trace operators on non homogeneous theta series that are siegel modular forms for the principal congruence subgroups of the symplectic group of level q n q then we prove that modular forms for the hecke subgroup of level q 0 n q that are linear combination of such theta series can also be expressed as combination of homogeneous theta series that are modular forms with respect to 0 n q