The present volume contains the proceedings of the workshop on minimax theory and applications that was held during the week 30 september 6 october 1996 at the g. The duration of a bond is a linear approximation of minus the percent change in its price given a 100 basis point change in interest rates. Consider an 8% 10year note at a price of 100 and a modified duration of 6. Fundamentals of convex analysis jeanbaptiste hiriart. When are nonconvex optimization problems not scary. May 08, 2016 a framework for analysing nonconvex optimization sanjeev arora, tengyu ma may 8, 2016 12 minute read previously rongs post and bens post show that noisy gradient descent can converge to local minimum of a nonconvex function, and in large polynomial time ge et al. Pdf nonconvexity, efficiency and equilibrium in exhaustible. Nonconvex economic dispatch using particle swarm optimization. Stampacchia international school of mathematics of the e. Pdf a onelayer recurrent neural network for realtime.
For option free coupon bonds, modified duration is better than maturity as a measure of the bonds sensitivity to changes in interest rates. Vuca the acronym vuca volatile, uncertain, complex and ambiguous accurately describes the conditions under which organisations, corporations and institutions operate in the world today. Finally, the numbers of operations required to verify these criteria are calculated and compared. Globally solving nonconvex quadratic programming problems via completely positive programming jieqiu cheny samuel burerz august 15, 2011 abstract nonconvex quadratic programming qp is an nphard problem that optimizes a general quadratic function over linear constraints. Minimizing nonconvex quadratic functions subject to bound constraints by hassan mohyuddin a thesis submitted to the johns hopkins university in conformity with the.
Longconvexity1 0 points 1 point 2 points 2 days ago inclusive government institutions which spread access to the power of the state to many different groups are the end goal. Bond prices change inversely with interest rates, and, hence, there is interest rate risk with bonds. Assuming only the standard transversality condition or a weaker version thereof, we prove local. Abstract convexity for nonconvex optimization duality.
Convexity relates to the interaction between a bonds price and its yield as it experiences changes in interest rates. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. We develop a new relaxation that exploits function structure while convexifying a product of n functions. In 2017 and banks are waking up to the fact that digital it architectures are a critical strategic differentiator.
Understanding duration and convexity of fixed income. Certain convexity questions in stochastic optimization. In practice, however, simple numerical methods often work surprisingly well in finding highquality solutions. Coarsetofine minimization of some common nonconvexities. In actuality, however, prices fall at an increasing rate as interest rates rise. Duration and convexity 443 that duration is a measure of interest rate risk is demonstrated as follows. We are interested in the case where ppn greatly exceeds the sample size n. Duration assumes a linear relationship between bond prices and changes in interest rates. Biconvex sets and optimization with biconvex functions a.
Introduction to non convex optimization yuanzhi li assistant professor, carnegie mellon university random date yuanzhi li cmu cmu random date 1 31. One method of measuring interest rate risk due to changes in market interest rates is by the full valuation approach, which simply calculates what bond prices will be if the interest rate changed by specific amounts. But avoid asking for help, clarification, or responding to other answers. Minimax theory and applications nonconvex optimization. Convexity solutions latest breaking news, pictures, videos, and special reports from the economic times. A first order criterion for pseudoconvexity and second order criteria for quasiconvexity and pseudoconvexity are given for twice differentiable functions on open convex sets.
Many problems arising from scientific and engineering applications can be naturally formulated as optimization problems, most of which are nonconvex. We also show that the strongly monotonic assumption of the mapping may not need for the existence of solutions. Application of the concepts of duration and convexity to portfolio will be clari. Coarsetofine minimization of some common nonconvexities 3 ing. Modified duration is the negative derivative of the present value function with respect to the effective interest rate, and expressed as a fraction of the present value. For a bond of face value usd1,000 with a semiannual coupon of 8. In economics, non convexity refers to violations of the convexity assumptions of elementary economics. Minimax theory and applications nonconvex optimization and. Neighborhoods article pdf available in mathematical notes 701. By applying these results to positively homogeneous functions it is shown that if f is a quadratic form which is quasiconvex on a convex c then f is convexifiable, that is, there exists a strictly increasing function k such that k.
Globally solving nonconvex quadratic programming problems via. Universal suffrage appears to really work for pluralistic political participation, and to that end it is great. The relationships between these second order criteria and other known criteria are also analysed. In economics, nonconvexity refers to violations of the convexity assumptions of elementary economics. On the relation between the nonconvexity of a set and the nonconvexity of its.
Transversality and alternating projections for nonconvex sets. Consequently, the results presented in this paper can be viewed as an improvement and refinement of some known. Pdf on the relation between the nonconvexity of a set and. The function structure is encapsulated using at most d over and underestimators. For nonconvex problems, obtaining a local minimizer is computationally hard in theory, never mind the global minimizer. The formula for calculating macaulay duration, where c coupon, r interest rate, p bond price, f the bonds face value and n is the number of periods is.
Duration and convexity, with illustrations and formulas. Face value 00 85480 33583 1679 bond price pvcf 101815 2 duration years 4 university of illinois, urbana champaign fin 300 spring 2009. This paper presents a particle swarm optimization pso to solve hard combinatorial constrained optimization problems such as nonconvex and discontinuous economic dispatch ed problem of large thermal power plants. This book is an abridged version of our twovolume opus convex analysis and minimization algorithms 18, about which we have received very positive feedback from users, readers, lecturers ever since it was published by springerverlag in 1993. While lockdowns from mumbai to chicago are credited with saving lives, the downsides are too evident now.
Katetovcorrection to on realvalued functions in topological spaces fundam. Nonconvexity, efficiency and equilibrium in exhaustible resource depletion article pdf available in environmental and resource economics 31. Basic economics textbooks concentrate on consumers with convex preferences that do not prefer extremes to inbetween values and convex budget sets and on producers with convex production sets. Although the paper investigates two example applications, the underlying ideas may be generalized to some other tasks. Bond duration and convexity simplified part 1 of 2.
Bond duration convexity practice problems answers 6 pages. Several measures have been suggested in the control equation of the classical pso by modifying its operators for better exploration and exploitation. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. How not to burn the whole house down to kill a rat. Bond duration convexity practice problems university of. Bond duration and convexity convexity continued bond duration and convexity convexity continued.
By using nonsmooth analysis knowledge, we provide the conditions for existence solutions of the variational inequalities problems in nonconvex setting. By applying these results to positively homogeneous functions it is shown that if f is a. Education in the vucaworld for the unprepared, the future is volatile, uncertain, complex and ambiguous. Lewisz august 3, 2015 abstract we consider the method of alternating projections for nding a point in the intersection of two closed sets, possibly nonconvex. Consequently, the results presented in this paper can be viewed as an improvement and refinement of some known results from the. A first order criterion for pseudo convexity and second order criteria for quasi convexity and pseudo convexity are given for twice differentiable functions on open convex sets. The sensitivity of the percentage bond price change to changes in interest.
A subordinated debenture is an unsecured bond that is junior to senior unsecured bonds, and hence there is more uncertainty pertaining to these securities. Duration and convexity are two tools used to manage the risk exposure of fixedincome investments. Necessary and sufficient conditions for convexity of lower semicontinuous quasiconvex functions are given. Paraconvexity and continuous selections sciencedirect. Nonconvexopmizaon through sequenalconvexprogramming. Thanks for contributing an answer to mathematics stack exchange. Transversality and alternating projections for nonconvex sets d. Grc strategy risk and compliance software iconvexity. A framework for analysing nonconvex optimization sanjeev arora, tengyu ma may 8, 2016 12 minute read previously rongs post and bens post show that noisy gradient descent can converge to local minimum of a nonconvex function, and in large polynomial time. Convexity definition of convexity by the free dictionary. This collection of papers is dedicated to the memory of gaetano fichera, a great mathematician and also a good friend to the editors. Majorana centre for scientific cul ture in erice italy.
Quantitative finance qf with matlab mario dellera scuola superiore santanna march 30, 2012 mario dellera quantitative finance. Duration and convexity 3 also referred to as debentures. Professor krannert school of management, purdue university. Pdf a performance attribution methodology for fixed income. The present value equation for an annual coupon bond is given by. Convexity solutions blogs, comments and archive news on. Minimizing nonconvex quadratic functions subject to bound. Proving that a specific function is quasiconvex mathoverflow. Pdf this paper presents a decisionmaking model described by a recurrent neural network for. Regrettably it took an unusual amount of time to bring this collec. The present volume, handbook of nonconvex analysis and applications, consists of thirteen chapters written by notable experts in the field, addressing essential recent developments in nonconvex analysis and its applications, and keeping a balance between major areas of theory, methods, and applications.
Abstract convexity for nonconvex optimization duality angelia nedic. In addition, we demonstrate that the minimizer of the convexi ed i. The discourse and controversies focus on the role of luck as opposed to teleological programs from telos, aim, that is, ones that rely on preset direction from formal. A bond is an instrument of indebtedness that obliges the bond issuer borrower to repay the lender creditor the borrowed assets plus the interest within a certain period of time fabozzi, 2000, p. Midpoint convexity does not imply convexity duplicate ask question asked 5 years, 11. Pdf on the relation between the nonconvexity of a set.
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