fuzzy mathematical programming for multi objective linear fractional programming problem the present paper deals with a solution procedure for multi objective linear fractional programming problems an equivalent multi objective linear programming form of the problem has been formulated in the proposed methodology using fuzzy set theoretic approach a procedure has been explored the proposed solution procedure has also been used to solve numerical examples

inherent bias and noise in the hough transform considering the hough transformation as a linear imaging process recasts certain well known problems provides a useful vocab ulary and possibly indicates a source of applicable literature on the behavior of the hough transformation in various forms of noise a consideration of the analytic form of peaks in parameter space sets the stage for the idea of using complementary negative votes to cancel off peak positive votes in parameter space thus sharpening peaks and reducing bias

methods for pricing american options under regime switching we analyze a number of techniques for pricing american options under a regime switching stochastic process the techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable in the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations numerical tests indicate that a fixed point policy iteration coupled with a direct control formulation is a reliable general purpose method finally we remark that we formulate the american problem as an abstract optimal control problem hence our results are applicable to more general problems as well

the adaptive hough transform we introduce the adaptive hough transform aht as an efficient way of implementing the hough transform ht method for the detection of 2 d shapes the aht uses a small accumulator array and the idea of a flexible iterative coarse to fine accumulation and search strategy to identify significant peaks in the hough parameter spaces the method is substantially superior to the standard ht implementation in both storage and computational requirements in this correspondence we illustrate the ideas of the aht by tackling the problem of identifying linear and circular segments in images by searching for clusters of evidence in 2 d parameter spaces we show that the method is robust to the addition of extraneous noise and can be used to analyze complex images containing more than one shape

some convergence results for howard s algorithm this paper deals with convergence results of howard s algorithm for the resolution of min a in mathcal a b a x c a 0 where b a is a matrix c a is a vector and mathcal a is a compact set we show a global superlinear convergence result under a monotonicity assumption on the matrices b a extensions of howard s algorithm for a max min problem of the form max b in mathcal b min a in mathcal a b a b x c a b 0 are also proposed in the particular case of an obstacle problem of the form min ax b x g 0 where a is an n times n matrix satisfying a monotonicity assumption we show the convergence of howard s algorithm in no more than n iterations instead of the usual 2 n bound still in the case of an obstacle problem we establish the equivalence between howard s algorithm and a primal dual active set algorithm m hintermuller k ito and k kunisch siam j optim 13 2002 pp 865 888 the algorithms are illustrated on the discretization of nonlinear pdes arising in the context of mathematical finance american option and merton s portfolio problem of front propagation problems and for the double obstacle problem

fuzzy approaches for multiple criteria linear fractional optimization a comment abstract in this note a fallacy of the second solution procedure for fuzzy multiple criteria linear fractional optimization described by luhandjula 1984 is noted

dual control monte carlo method for tight bounds of value function in regime switching utility maximization abstract in this paper we study the dual control approach for the optimal asset allocation problem in a continuous time regime switching market we find the lower and upper bounds of the value function that is a solution to a system of fully coupled nonlinear partial differential equations these bounds can be tightened with additional controls to the dual process we suggest a monte carlo algorithm for computing the tight lower and upper bounds and show the method is effective with a variety of utility functions including power non hara and yaari utilities the latter two utilities are beyond the scope of any current methods available in finding the value function

a restricted class of multiobjective linear fractional programming problems abstract in this paper a restricted class of multiobjective linear fractional programming problems in the sense that the denominators are identical is investigated a numerical example is presented to illustrate the solution procedure

discretization errors in the hough transform abstract straight line segments in a two dimensional image can be detected with the hough transform by searching peaks in a parameter space the influence on the hough transform of the quantization of the parameter space the quantization of the image and the width of the line segment is investigated in this paper the hough transform was improved by o gorman and clowes by taking into account the gradient direction the resulting scatter of the peaks can be reduced by using a weighting function in the transform examples of asbestos preparations are given

taylor series approach to fuzzy multiobjective linear fractional programming this paper presents the use of a taylor series for fuzzy multiobjective linear fractional programming problems fmolfp the taylor series is a series expansion that a representation of a function in the proposed approach membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a taylor series are unified thus the problem is reduced to a single objective practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach

multiresolution hough transform an efficient method of detecting patterns in images a new multiresolution coarse to fine search algorithm for efficient computation of the hough transform is proposed the algorithm uses multiresolution images and parameter arrays logarithmic range reduction is proposed to achieve faster convergence discretization errors are taken into consideration when accumulating the parameter array this permits the use of a very simple peak detection algorithm comparative results using three peak detection methods are presented tests on synthetic and real world images show that the parameters converge rapidly toward the true value the errors in rho and theta as well as the computation time are much lower than those obtained by other methods since the multiresolution hough transform mht uses a simple peak detection algorithm the computation time will be significantly lower than other algorithms if the time for peak detection is also taken into account the algorithm can be generalized for patterns with any number of parameters

a goal programming procedure for fuzzy multiobjective linear fractional programming problem abstract this paper presents a goal programming gp procedure for fuzzy multiobjective linear fractional programming fmolfp problems in the proposed approach which is motivated by mohamed fuzzy sets and systems 89 1997 215 gp model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated in the solution process the method of variable change on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming lgp methodology the approach is illustrated by two numerical examples

fuzzy approaches for multiple objective linear fractional optimization abstract the problem of finding a solution to a multiple objective linear fractional program arises in several real world situations in this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness after representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program techniques of fuzzy linear programming may be used to reach a satisfactory solution it is shown that under reasonable restrictions this solution is efficient pareto optimal for the original problem numerical examples are also included for illustration

maximal use of central differencing for hamilton jacobi bellman pdes in finance in order to ensure convergence to the viscosity solution the standard method for discretizing hamilton jacobi bellman partial differential equations uses forward backward differencing for the drift term in this paper we devise a monotone method which uses central weighting as much as possible in order to solve the discretized algebraic equations we have to maximize a possibly discontinuous objective function at each node nevertheless convergence of the overall iteration can be guaranteed numerical experiments on two examples from the finance literature show higher rates of convergence for this approach compared to the use of forward backward differencing only

combined fixed point and policy iteration for hamilton jacobi bellman equations in finance implicit methods for hamilton jacobi bellman hjb partial differential equations give rise to highly nonlinear discretized algebraic equations the classic policy iteration approach may not be efficient in many circumstances in this article we derive sufficient conditions to ensure convergence of a combined fixed point policy iteration scheme for the solution of discretized equations numerical examples are included for a singular stochastic control problem arising in insurance a guaranteed minimum withdrawal benefit where the underlying risky asset follows a jump diffusion and an american option assuming a regime switching process

a numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit gmwb in this paper we outline an impulse stochastic control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit gmwb assuming the policyholder is allowed to withdraw funds continuously we develop a numerical scheme for solving the hamilton jacobi bellman hjb variational inequality corresponding to the impulse control problem we prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem provided a strong comparison result holds the scheme can be easily generalized to price discrete withdrawal contracts numerical experiments are conducted which show a region where the optimal control appears to be non unique

convergence properties of policy iteration this paper analyzes asymptotic convergence properties of policy iteration in a class of stationary infinite horizon markovian decision problems that arise in optimal growth theory these problems have continuous state and control variables and must therefore be discretized in order to compute an approximate solution the discretization may render inapplicable known convergence results for policy iteration such as those of puterman and brumelle math oper res 4 1979 pp 60 69 under certain regularity conditions we prove that for piecewise linear interpolation policy iteration converges quadratically also under more general conditions we establish that convergence is superlinear we show how the constants involved in these convergence orders depend on the grid size of the discretization these theoretical results are illustrated with numerical experiments that compare the performance of policy iteration and the method of successive approximations

a convergent difference scheme for a class of partial integro differential equations modeling pricing under uncertainty in this paper we present a finite difference scheme to approximate viscosity solutions of a class of partial integro differential equations describing pricing under model uncertainty we establish

a policy iteration algorithm for the american put option and free boundary control problems abstract we develop a solution method for american put options that directly employs the policy iteration principle of dynamic programming the method iteratively improves exercise policies obtains monotonically increasing value functions and converges quadratically under reasonable assumptions we present a numerical implementation that exhibits these features the same principle is also applied to obtain a monotonically improving policy iteration scheme for general free boundary optimal control problems

a penalty method for american options with jump diffusion processes the fair price for an american option where the underlying asset follows a jump diffusion process can be formulated as a partial integral differential linear complementarity problem we develop an implicit discretization method for pricing such american options the jump diffusion correlation integral term is computed using an iterative method coupled with an fft while the american constraint is imposed by using a penalty method we derive sufficient conditions for global convergence of the discrete penalized equations at each timestep finally we present numerical tests which illustrate such convergence