superfast solution of linear convolutional volterra equations using qtt approximation we address a linear fractional differential equation and develop effective solution methods using algorithms for the inversion of triangular toeplitz matrices and the recently proposed qtt format the inverses of such matrices can be computed by the divide and conquer and modified bini s algorithms for which we present the versions with the qtt approximation we also present an efficient formula for the shift of vectors given in qtt format which is used in the divide and conquer algorithm as a result we reduce the complexity of inversion from the fast fourier level o n log n to the speed of superfast fourier transform i e o log 2 n the results of the paper are illustrated by numerical examples

local stability conditions for t s fuzzy time delay systems using a homogeneous polynomial approach abstract local stability conditions for time delay t s fuzzy systems are proposed by use of a homogeneous polynomial approach lesser conservatism can be expected based on the derived stability criteria due to the following three factors a a new fuzzy lyapunov krasovskii functional is constructed which contains a homogeneous polynomially parameter dependent matrix of degree 2 b the off diagonal matrix in reciprocal convexity lemma is extended to a homogeneous polynomially parameter dependent matrix and c local stability conditions for time delay t s fuzzy systems are proposed to overcome the difficulty of dealing with the time derivative of membership functions finally two numerical examples illustrate the effectiveness of the proposed methods

optimal portfolio and consumption decisions for a small investor on a finite horizon a general consumption investment problem is considered for an agent whose actions cannot affect the market prices and who strives to maximize total expected discounted utility of both consumption

dynamic parallel distributed compensation for takagi sugeno fuzzy systems an lmi approach abstract this paper presents a unified systematic framework for designing dynamic feedback controllers for nonlinear systems described by takagi sugeno t s models both stabilization and multi objective control synthesis problems have been addressed the control laws are in the form of so called dynamic parallel distributed compensation dpdc which are essentially nonlinear dynamic feedback controllers the associated control synthesis problems are formulated as linear matrix inequality lmi problems i e the parameters of the dpdc controllers are obtained from a set of lmi conditions the approach in this paper can also be applied to hybrid or switching systems

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

optimal bankruptcy time and consumption investment policies on an infinite horizon with a continuous debt repayment until bankruptcy in this paper we consider the optimization problem of an agent who wants to maximize the total expected discounted utility from consumption over an infinite horizon the agent is under obligation to pay a debt at a fixed rate until he she declares bankruptcy at that point after paying a fixed cost the agent will be able to keep a certain fraction of the present wealth and the debt will be forgiven the selection of the bankruptcy time is taken to be at the discretion of the agent the novelty of this paper is that at the time of bankruptcy the wealth process has a discontinuity and that the agent continues to invest and consume after bankruptcy we show that the solution of a free boundary problem satisfying some additional conditions is the value function of the above optimization problem particular examples such as the logarithmic and the power utility functions will be provided and in these cases explicit forms will be given for the optimal bankruptcy time investment and consumption processes

optimal investment consumption and timing of annuity purchase under a preference change abstract in this paper we study the optimal investment and consumption strategies for a retired individual who has the opportunity of choosing a discretionary stopping time to purchase an annuity we assume that the individual receives a fixed annuity income and changes his her preference after paying a fixed cost for annuitization by using the martingale method and the variational inequality method we tackle this problem and obtain the optimal strategies and the value function explicitly for the case of constant force of mortality and constant relative risk aversion crra utility function

networked control for a class of t s fuzzy systems with stochastic sensor faults this paper is concerned with networked control for a class of t s fuzzy systems with stochastic sensor faults first a unified model of networked control system is proposed which has two significant features a the fault statistics of each sensor is individually quantified and b stochastic sensor faults and nonideal network quality of services qos such as data dropout and network induced delay are coupled in a unified framework secondly based on the lyapunov krasovskii functional and the stochastic analysis technique sufficient network qos dependent conditions are derived for the stability analysis and controller design respectively moreover a modified cone complementary linearisation ccl algorithm is also introduced to solve the nonlinear matrix inequalities in the controller design finally two examples are given to demonstrate the effectiveness of the proposed method

a novel identification method for takagi sugeno fuzzy model abstract based on the xie beni index and an improved particle swarm optimization algorithm a novel identification method for the takagi sugeno fuzzy model is proposed in this paper firstly xie beni indices with a fuzzy c means clustering algorithm are adopted to find the rule number of the takagi sugeno fuzzy model by utilizing the particle swarm optimization algorithm the initial membership function and the consequent parameters of the fuzzy model are obtained in addition through an improved fuzzy c regression model and orthogonal least square method the premise structure and consequent parameters can be obtained to establish the takagi sugeno fuzzy model some well known models are used to demonstrate that the proposed method outperforms some existing methods

communication delay distribution dependent networked control for a class of t s fuzzy systems this paper investigates a robust networked control for a class of takagi sugeno t s fuzzy systems the controller design specifically takes probabilistic interval distribution of the communication delay into account a general framework of networked control is first proposed the two main features are 1 the zero order hold can choose the latest control input signal when the packets received are out of order and 2 as the result of 1 the models of the all kinds of uncertainties in networked signal transfer including network induced delay and data packet dropout are under a unified framework next if the probability distribution of communication delay is known or specified in a design process sufficient stability conditions for networked t s fuzzy systems are derived which are based on the lyapunov theory following this a stabilizing controller design method is developed which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well finally a numerical example is used to show the application of the theoretical results obtained in this paper

dynamic mean variance portfolio selection with no shorting constraints this paper is concerned with mean variance portfolio selection problems in continuous time under the constraint that short selling of stocks is prohibited the problem is formulated as a stochastic optimal linear quadratic lq control problem however this lq problem is not a conventional one in that the control portfolio is constrained to take nonnegative values due to the no shorting restriction and thereby the usual riccati equation approach involving a completion of squares does not apply directly in addition the corresponding hamilton jacobi bellman hjb equation inherently has no smooth solution to tackle these difficulties a continuous function is constructed via two riccati equations and then it is shown that this function is a viscosity solution to the hjb equation solving these riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean variance problem an example illustrating these results is also presented

stability analysis of product t methods for abel integral equations of the second kind stability analysis of product methods for abel integral equations of the second kind based on the test equation y t 1 lambda int limits 0 1 frac y s t s alpha ds t geqq 0 0 0 and we investigate whether this property is inherited by numerical approximations toy

on monotone abel volterra integral equations on the half line in this paper we reanalyze the trapezoidal method for the solution of nonlinear abel volterra integral equations on the half line we prove the convergence of the method in the uniform norm provided the nonlinearity is lipschitz continuous and strictly monotone

an optimal consumption investment and voluntary retirement choice problem with disutility and subsistence consumption constraints a dynamic programming approach abstract in this paper we investigate an optimal consumption portfolio problem of an agent with voluntary retirement and subsistence consumption constraints before retirement we assume that the agent s utility function of consumption is of crra type and the agent suffers a utility loss from labor before retirement we use the dynamic programming method to obtain explicit forms of the optimal consumption portfolio and retirement time

a stochastic control approach to the pricing of options we construct a stochastic control model of a portfolio in which the investor may invest in stock call options on the stock or risk free bonds he may also borrow funds we assume that the investor is attempting to maximize expected utility of total wealth at expiration of the options where the utility function is given as wealth to the power 0 1 this includes both the risk averse and risk neutral cases we allow the borrowing interest rate r to be distinct from the lending interest rate r we make two fundamental assumptions i the investor cannot achieve infinite expected utility of wealth in finite time stable markets and ii the market will set the option price to minimize the investor s maximal expected utility of wealth i e options are priced using a minimax strategy the market is stable only when r r we prove in the case r r and 1 that the minimax european call option price ft s is given as the solution of the black scholes equation ft i i 2s2fss i s fs i f 0 where i r when r i 2 1 i r when i 2 1 r and i i 2 1 if r i 2 1 r the parameter is the stock return drift and i is the stock return diffusion if r r then the call option price must by stable markets always be the black scholes price with rate r in the risk neutral 1 case we must have r r for a stable market and the option price given by the black scholes equation but with i explicit solutions are presented and the optimal portfolios and returns are also derived comparable results are obtained for american call options which can be exercised at any time up to and including the expiration date in this case the option pricing function is shown to be the solution of an obstacle problem

h_ infty filter design for a class of networked control systems via t s fuzzy model approach this paper is concerned with h design for a class of networked control systems ncss with multiple state delays via the takagi sugeno t s fuzzy model the transfer delays and packet loss that are induced by the limited bandwidth of communication networks are considered the focus of this paper is on the analysis and design of a full order h filter such that the filtering error dynamics are stochastically stable and a prescribed h attenuation level is guaranteed sufficient conditions are established for the existence of the desired filter in terms of linear matrix inequalities lmis an example is given to illustrate the effectiveness and applicability of the proposed design method

optimal consumption from investment and random endowment in incomplete semimartingale markets we consider the problem of maximizing expected utility from consumption in a con strained incomplete semimartingale market with a random endowment process and establish a general existence and uniqueness result using techniques from convex duality the notion of as ymptotic elasticity of kramkov and schachermayer is extended to the time dependent case by imposing no smoothness requirements on the utility function in the temporal argument we can treat both pure consumption and combined consumption terminal wealth problems in a com mon framework to make the duality approach possible we provide a detailed characterization of the enlarged dual domain which is reminiscent of the enlargement of l 1 to its topological bidual l 1 a space of finitely additive measures as an application we treat a constrained ito process market model as well as a totally incomplete model

network based h control for t s fuzzy systems with an adaptive event triggered communication scheme abstract this paper extends the prior work of discrete event triggered communication for networked t s fuzzy systems where the next communication instant is determined by an event triggered communication scheme with a constant threshold and the premises of t s fuzzy systems and parallel distribution compensation pdc fuzzy control rules are synchronous firstly an adaptive event triggered communication scheme for ncss is presented which relaxes the assumption of the prior work that the threshold of event triggered communication scheme is a preselected constant secondly an asynchronous premise re construct method for networked t s fuzzy systems is proposed which relaxes the assumption of the prior work that the premises of the plant and the pdc control rules are synchronous we show that the number of transmitted packets generated by the proposed scheme is smaller than those generated by some existing ones while ensuring the desired control performance simulations show the effectiveness of the proposed method

finite time h asynchronous state estimation for discrete time fuzzy markov jump neural networks with uncertain measurements abstract this paper is concerned with the problem of the h asynchronous state estimation for fuzzy markov jump neural networks fmjnns with uncertain measurements over a finite time interval in terms of a bernoulli distributed white sequence the phenomenon of the randomly occurring uncertainties in the output equation is represented by exploiting a random variable with known occurrence probabilities the main focus of this paper is to present a state estimator such that the resulting error system is finite time bounded and satisfies an h performance requirement then by employing the stochastic analysis technique sufficient conditions are provided to ensure that the state estimator is designed by means of solving a convex optimization problem an example is finally given to explain the effectiveness and potentiality of the proposed design method

delay dependent stabilization for stochastic fuzzy systems with time delays this paper is concerned with the delay dependent stabilization problem for a class of time delay stochastic fuzzy systems the time delays are assumed to appear in both the state and the control input the purpose is the design of a state feedback fuzzy controller such that the resulting closed loop system is asymptotically stable in the mean square a delay dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities lmis by solving these lmis a desired controller can be obtained finally a numerical example is given to demonstrate the effectiveness of the present results

novel stabilization criteria for t s fuzzy systems with affine matched membership functions this paper presents a new parallel distributed compensation controller design approach for t s takagi sugeno fuzzy control systems with affine matched membership functions in the system and controller in the new fuzzy control affine transformed membership functions are adopted by scaling and biasing the original membership functions of the system stabilization and performance criterion of the closed loop t s fuzzy systems are obtained through a new parameterized linear matrix inequality which is rearranged by affine matched membership functions the conservativeness of stabilization condition for the t s fuzzy system is significantly relaxed by utilizing the constraints condition of the controllers membership functions which is determined from the difference of each transformed membership function in addition the controller gain is reconstructed by a decision variable separation technique with two different free weighting matrices without any scaling parameter the superiority of proposed method is verified through numerical examples

utility maximization with discretionary stopping utility maximization problems of mixed optimal stopping control type are considered which can be solved by reduction to a family of related pure optimal stopping problems sufficient conditions for the existence of optimal strategies are provided in the context of continuous time ito process models for complete markets the mathematical tools used are those of optimal stopping theory continuous time martingales convex analysis and duality theory several examples are solved explicitly including one which demonstrates that optimal strategies need not always exist

novel stability conditions for discrete time t s fuzzy systems this paper is concerned with the issue of developing a novel strategy to reduce the conservatism of stability conditions for discrete time takagi sugeno t s fuzzy systems unlike the previous ones which are almost quadratic with respect to the state vector a new class of lyapunov functions is proposed which is quadratic with respect to the kronecker products of the state vector thus including almost the existing ones found in the literature as special cases by combining the characterizations of homogeneous matrix polynomials and the properties of membership functions relaxed stability conditions are derived in the form of linear matrix inequalities which can be efficiently solved by the convex optimization techniques finally a numerical example is provided to illustrate the effectiveness of the proposed approach

stability results for collocation methods for volterra integral equations abstract stability behavior is investigated for polynomial spline collocation applied to volterra integral equations with special emphasis on a weakly singular test equation the characterization of the corresponding stability domain is related to stability results for solutions of finite recursion relations as they occur for methods applied to ordinary differential equations estimates of the stability domains are established and as a consequence conditions for a 2 stability are obtained exploiting these estimates collocation approximations with constant linear and continuous splines are considered in more depth and several numerical illustrations are presented

sampled data fuzzy stabilization of nonlinear systems under nonuniform sampling this paper investigates the sampled data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in takagi sugeno fuzzy form at least locally a new method for designing parallel distribution compensation fuzzy controller is proposed which just requires that the nonlinear function is locally lipschitz by considering the sample and hold behavior of the system and using jensen s integral inequality an inequality constrain condition is derived from the locally lipschitz property further by defining a time dependent lyapunov krasovskii functional term a new technique instead of the use of s procedure is developed and stabilization conditions for state feedback and observer based output feedback under nonuniform sampling are obtained compared with the existing ones the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions but contains less conservatism and less numerical complexity as well finally some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results

non fragile memory filtering of t s fuzzy delayed neural networks based on switched fuzzy sampled data control abstract this paper deals with the non fragile memory filtering issue of t s fuzzy delayed neural networks with randomly occurring time varying parameters uncertainties and variable sampling rates compared with existing sampled data control schemes an improved switched fuzzy memory sampled data control protocol is designed for the first time which involves not only a signal transmission delay but also switched topologies by developing some new terms and taking full advantage of the variable characteristics related to the actual sampling pattern a modified loose looped fuzzy membership functions fmfs dependent lyapunov krasovskii functional lkf is constructed based on the information of the time derivative of fmfs meanwhile some relaxed matrices chosen in lkf are not consequentially positive definite moreover with the lkf methodology and employing the developed estimation technique several optimized control algorithms with both a larger sampling period and upper bound of time varying delays for achieving the stabilization of the resultant t s fuzzy delayed neural networks are derived finally a numerical example is presented to demonstrate the superiority and applicability of the theoretical results

improved delay dependent robust stabilization conditions of uncertain t s fuzzy systems with time varying delay this paper aims to develop simplified yet improved delay dependent robust control for uncertain t s fuzzy systems with time varying delay this is achieved through constructing new lyapunov krasovskii functionals and improving jensen s inequality unlike existing work in this area the approach developed in this paper employs neither free weighing matrices nor model transformations as a result simplified yet improved stability conditions are obtained for t s fuzzy systems with norm bounded type uncertainties for controller synthesis of the fuzzy systems the stabilization problem with memoryless state feedback control is solved via utilizing a cone complementarity minimization algorithm numerical examples are given to demonstrate the effectiveness of the proposed approach

comparison of optimal portfolios with and without subsistence consumption constraints abstract we present the effects of the subsistence consumption constraints on a portfolio selection problem for an agent who is free to choose when to retire with a constant relative risk aversion crra utility function by comparing the previous studies with and without the constraints expressed by the minimum consumption requirement the changes of a retirement wealth level and the amount of money invested in the risky asset are derived explicitly as a result the subsistence constraints always lead to lower retirement wealth level but do not always induce less investment in the risky asset this implies that even though the agent who has a restriction on consumption retires with lower wealth level she invests more money near the retirement when her risk aversion lies inside a certain range

robust h control for nonlinear systems over network a piecewise analysis method a piecewise analysis method pam is proposed to investigate the h performance analysis and h control design for nonlinear networked control systems nncss which are presented in the form of t s fuzzy model with time varying input delay different from the existing method in dealing with the time varying delay the whole variation interval of the delay is divided into two subintervals with equal length respecting for the delay belonging each subinterval new criteria on h performance analysis of the nncss are obtained by checking the variation of the derivative of the lyapunov functional in the two subintervals then criteria for the h controller design are obtained by using the convexity properties of the matrix inequality and some other new analysis techniques which are shown in terms of nonlinear matrix inequalities and can be solved by using a cone complementarity liberalization method as application of the derived results h controller design is carried out for the nonlinear mass spring system discussion shows that the proposed method is less conservative than the existing references

relaxed lmi based stability conditions for takagi sugeno fuzzy control systems using regional membership function shape dependent analysis approach this paper presents relaxed stability conditions for takagi sugeno t s fuzzy model based control systems it is assumed that the stability conditions are represented by some inequalities in the form of a p dimensional fuzzy summation to investigate the system stability the inequalities are expanded to n dimensional fuzzy summation n ges p the boundary and regional informations of membership functions are then utilized for relaxation of stability analysis results two analysis approaches are proposed in this paper the first approach is called the global membership function shape dependent approach in which the lower and upper bounds of the membership functions and its products from 2 to n in the full operating domain are considered in the stability analysis the second approach is named as the regional membership function shape dependent approach in which the operating region is partitioned to subregions and the boundary information of membership functions on each operating subregion is employed to facilitate the stability analysis in both approaches by the help of the boundary and or regional information of the membership functions some inequality constraints in the form of multidimensional fuzzy summation containing some slack matrices are constructed stability conditions in the form of linear matrix inequalities lmis are derived numerical examples are given to demonstrate the effectiveness of the proposed stability conditions

optimal consumption and portfolio selection problem with downside consumption constraints abstract we study a general optimal consumption and portfolio selection problem of an infinitely lived investor whose consumption rate process is subjected to downside constraint that is her consumption rate is greater than or equals to some positive constant we obtain the general optimal policies in an explicit form using martingale method and feynman kac formula we derive some numerical results of optimal consumption and portfolio in the special case of a constant relative risk aversion crra utility function

stochastic portfolio optimization with default risk abstract a stochastic portfolio optimization problem with default risk on an infinite time horizon is investigated the default risk premium and the default intensity corresponding to the defaultable bond are assumed to rely on a stochastic factor formulated by a diffusion process we study the optimal allocation and consumption policies to maximize the infinite horizon expected discounted non log hara utility of the consumption and we use the dynamic programming principle to derive the hamilton jacobi bellman hjb equation then we explore the hjb equation by employing a so called sub super solution approach the optimal allocation and consumption policies are finally presented in a verification theorem and also a numerical simulation is given at the end of the paper

sampled data filtering of takagi sugeno fuzzy neural networks with interval time varying delays abstract this paper is concerned with sample data filtering of t s fuzzy neural networks with interval time varying delays which is formed by a fuzzy plant with time delay and a sampled data fuzzy controller connected in a closed loop a takagi sugeno t s fuzzy model is adopted for the neural networks and the sampled data fuzzy controller is designed for a t s fuzzy system to develop the guaranteed cost control a new stability condition of the closed loop system is guaranteed in the continuous time lyapunov sense and its sufficient conditions are formulated in terms of linear matrix inequalities by using a descriptor representation the sampled data fuzzy control system with time delay can be reduced to ease the stability analysis which effectively leads to a smaller number of lmi stability conditions information of the membership functions of both the fuzzy plant model and fuzzy controller are considered which allows arbitrary matrices to be introduced to ease the satisfaction of the stability conditions by a newly proposed inequality bounding technique the fuzzy sampled data filtering performance analysis is carried out such that the resultant neural networks is asymptotically stable numerical example and simulation result are given to illustrate the usefulness and effectiveness of the proposed theoretical results

optimal portfolio consumption and retirement decision under a preference change we investigate an optimal portfolio consumption and retirement decision problem in which an economic agent can determine the discretionary stopping time as a retirement time with constant labor wage and disutility we allow the preference of the agent to be changed before and after retirement it is assumed that the agent s coefficient of relative risk aversion becomes higher after retirement under a constant relative risk aversion crra utility function we obtain the optimal policies in closed forms using martingale methods and variational inequality methods we give some numerical results of the optimal policies we also consider the relation between the level of disutility and the labor wage with the optimal retirement wealth level

optimal investment consumption and retirement choice problem with disutility and subsistence consumption constraints in this paper we consider a general optimal consumption portfolio selection problem of an infinitely lived agent whose consumption rate process is subject to subsistence constraints before retirement that is her consumption rate should be greater than or equal to some positive constant before retirement we integrate three optimal decisions which are the optimal consumption the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model we obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem we treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches we also derive closed forms of the optimal wealth processes before and after retirement some numerical examples are presented for the case of constant relative risk aversion crra utility class

distributed non fragile filtering in sensor networks with energy constraints this paper investigates the distributed filtering problem for sensor networks with energy constraint and filter gain variation firstly two strategies are proposed to reduce energy consumption i e the measurement size and the transmission rate reduction strategies to reduce the measurement size a useful measurement selection policy is introduced to choose which element of local measurements is transmitted the selected measurement which has a smaller size than the original one is then stochastically transmitted in order to reflect the imprecision in filter implementation the additive filter gain variation problem is considered based on the switched system approach and some stochastic system analysis methods a sufficient condition is obtained such that the filtering error system is exponentially stable in the mean square sense and a prescribed h performance level is guaranteed filter gains are shown to be determined by solving a set of linear matrix inequalities lmis finally a simulation example is given to demonstrate the effectiveness of the proposed design

relaxed stability and stabilization conditions of networked fuzzy control systems subject to asynchronous grades of membership this paper presents relaxed stability and stabilization conditions for takagi sugeno t s fuzzy systems under network environments subject to asynchronous grades of membership because of the introduction of a communication network the favorable property in the point to point connection that is sharing the identical premises in the fuzzy plant and the fuzzy controllers cannot be arbitrarily employed to widen the applicability of the fuzzy control method under network environments a novel method is provided to reconstruct the synchronous time scale grades of membership at the controller as those in the plant as a result the aforementioned favorable property can be conditionally used in the derivation of the stability and stabilization criteria for the system under consideration controlled over a communication network numerical examples have been given to illustrate the effectiveness of the proposed approach

stabilization of networked control systems with a logic zoh the technical note is concerned with the stabilization problem of networked control systems a general framework is proposed firstly where the zero order hold has the logical capability of choosing the newest control input packet the continuous time process is discretized as a system with input delays then a sufficient condition for testing the stability of the discretized system and two sufficient conditions for designing a stabilizing controller are established based upon the lyapunov theory finally numerical examples and simulations are used to illustrate the developed theory

uniform error estimates of galerkin methods for monotone abel volterra integral equations on the half line we consider galerkin methods for monotone abel volterra integral equations of the second kind on the half line the l2 theory follows from kolodner s theory of monotone hammerstein equations we derive the loo theory from the l2 theory by relating the l2and loo spectra of operators of the form x b ax to one another here denotes convolution and b e l1 and a e loo as an extra condition we need b t o t a 1 with a 0 we also prove the discrete analogue in particular we verify that the galerkin matrix satisfies the discrete conditions

a kind of optimal investment problem under inflation and uncertain time horizon abstract in this paper we study a kind of optimal investment problem under inflation and uncertain time horizon it can be generally formulated into a stochastic optimal control problem in particular for the constant relative risk aversion utility we employ the method of completion of squares to give an explicit form of optimal portfolio and maximum utility by the solution of a stochastic riccati equation whose wellposedness is obtained and also of significance in its own right the most distinguishing result of our work is that the randomness of exit time actually affects not only the optimal portfolio but also the maximum utility in the case of stochastic market parameters moreover we present several numerical examples to show the application of theoretical results and further discuss the influence of inflation and random time horizon from the economic viewpoint

a family of methods for abel integral equations of the second kind abstract a class of methods depending on some parameters are introduced for the numerical solution of the abel integral equations of the second kind some bounds on the parameters are determined so that the corresponding methods have infinite stability intervals

a perspective on the numerical treatment of volterra equations abstract we discuss the properties and numerical treatment of various types of volterra and abel volterra integral and integro differential equations

a dynamic programming approach to constrained portfolios this paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption our first contribution is that we solve the problems by dynamic programming which is in contrast to the existing literature that applies the martingale method more precisely we construct the non separable value function by formalizing the optimal constrained terminal wealth to be a conjectured contingent claim on the optimal non constrained terminal wealth this is relevant by itself but also opens up the opportunity to derive new solutions to constrained problems as a second contribution we thus derive new results for non strict constraints on the shortfall of intermediate wealth and or consumption

objective comparisons of the optimal portfolios corresponding to different utility functions abstract this paper considers the effects of some frequently used utility functions in portfolio selection by comparing the optimal investment outcomes corresponding to these utility functions assets are assumed to form a complete market of the black scholes type under consideration are four frequently used utility functions the power logarithm exponential and quadratic utility functions to make objective comparisons the optimal terminal wealths are derived by integration representation the optimal strategies which yield optimal values are obtained by the integration representation of a brownian martingale the explicit strategy for the quadratic utility function is new the strategies for other utility functions such as the power and the logarithm utility functions obtained this way coincide with known results obtained from merton s dynamic programming approach