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. 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. Pdf on the relation between the nonconvexity of a set and. Nonconvex economic dispatch using particle swarm optimization. We develop a new relaxation that exploits function structure while convexifying a product of n functions. How not to burn the whole house down to kill a rat. Bond duration convexity practice problems answers 6 pages.
Duration and convexity 3 also referred to as debentures. Education in the vucaworld for the unprepared, the future is volatile, uncertain, complex and ambiguous. Pdf nonconvexity, efficiency and equilibrium in exhaustible. Nonconvexopmizaon through sequenalconvexprogramming. Assuming only the standard transversality condition or a weaker version thereof, we prove local. Professor krannert school of management, purdue university.
Quantitative finance qf with matlab mario dellera scuola superiore santanna march 30, 2012 mario dellera quantitative finance. Necessary and sufficient conditions for convexity of lower semicontinuous quasiconvex functions are given. 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. Bond duration convexity practice problems university of. In practice, however, simple numerical methods often work surprisingly well in finding highquality solutions. Pdf a performance attribution methodology for fixed income. Katetovcorrection to on realvalued functions in topological spaces fundam. Pdf a onelayer recurrent neural network for realtime. By applying these results to positively homogeneous functions it is shown that if f is a. 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. For nonconvex problems, obtaining a local minimizer is computationally hard in theory, never mind the global minimizer.
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. Just as with dollar duration, the dollar convexity of the portfolio is the sum of the dollar convexities of the component zeroes. On growth conditions for quasiconvex integrands parth soneji. Convexity definition of convexity by the free dictionary. The relationships between these second order criteria and other known criteria are also analysed. Paraconvexity and continuous selections sciencedirect. Minimizing nonconvex quadratic functions subject to bound constraints by hassan mohyuddin a thesis submitted to the johns hopkins university in conformity with the. A first order criterion for pseudoconvexity and second order criteria for quasiconvexity and pseudoconvexity are given for twice differentiable functions on open convex sets.
Duration and convexity are two tools used to manage the risk exposure of fixedincome investments. Duration measures the bonds sensitivity to interest rate changes. For zeroes, duration is roughly equal to maturity, convexity is roughly equal to maturity squared. 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. But avoid asking for help, clarification, or responding to other answers. Although the paper investigates two example applications, the underlying ideas may be generalized to some other tasks.
Several measures have been suggested in the control equation of the classical pso by modifying its operators for better exploration and exploitation. Minimizing nonconvex quadratic functions subject to bound. 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. In actuality, however, prices fall at an increasing rate as interest rates rise. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. 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. Duration and convexity, with illustrations and formulas.
A subordinated debenture is an unsecured bond that is junior to senior unsecured bonds, and hence there is more uncertainty pertaining to these securities. Abstract convexity for nonconvex optimization duality angelia nedic. For option free coupon bonds, modified duration is better than maturity as a measure of the bonds sensitivity to changes in interest rates. Minimax theory and applications nonconvex optimization and. Coarsetofine minimization of some common nonconvexities 3 ing. Finally, the numbers of operations required to verify these criteria are calculated and compared.
Neighborhoods article pdf available in mathematical notes 701. The sensitivity of the percentage bond price change to changes in interest. In addition, we demonstrate that the minimizer of the convexi ed i. Convexity solutions latest breaking news, pictures, videos, and special reports from the economic times. Abstract convexity for nonconvex optimization duality. Duration and convexity 443 that duration is a measure of interest rate risk is demonstrated as follows. Certain convexity questions in stochastic optimization. Bond duration and convexity convexity continued bond duration and convexity convexity continued.
Biconvex sets and optimization with biconvex functions a. In economics, non convexity refers to violations of the convexity assumptions of elementary economics. Transversality and alternating projections for nonconvex sets d. Duration assumes a linear relationship between bond prices and changes in interest rates. In 2017 and banks are waking up to the fact that digital it architectures are a critical strategic differentiator.
Application of the concepts of duration and convexity to portfolio will be clari. Midpoint convexity does not imply convexity duplicate ask question asked 5 years, 11. 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. 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. 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. Coarsetofine minimization of some common nonconvexities. Relationship between semiconvexity and lipschitz continuity. Many problems arising from scientific and engineering applications can be naturally formulated as optimization problems, most of which are nonconvex.
We are interested in the case where ppn greatly exceeds the sample size n. Regrettably it took an unusual amount of time to bring this collec. Majorana centre for scientific cul ture in erice italy. Consider an 8% 10year note at a price of 100 and a modified duration of 6. Vuca the acronym vuca volatile, uncertain, complex and ambiguous accurately describes the conditions under which organisations, corporations and institutions operate in the world today. Pdf this paper presents a decisionmaking model described by a recurrent neural network for. Nonconvexity, efficiency and equilibrium in exhaustible resource depletion article pdf available in environmental and resource economics 31. Introduction to non convex optimization yuanzhi li assistant professor, carnegie mellon university random date yuanzhi li cmu cmu random date 1 31. Consequently, the results presented in this paper can be viewed as an improvement and refinement of some known. 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. While lockdowns from mumbai to chicago are credited with saving lives, the downsides are too evident now. Minimax theory and applications nonconvex optimization. Transversality and alternating projections for nonconvex sets. When are nonconvex optimization problems not scary.
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. Fundamentals of convex analysis jeanbaptiste hiriart. 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 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. This collection of papers is dedicated to the memory of gaetano fichera, a great mathematician and also a good friend to the editors. Universal suffrage appears to really work for pluralistic political participation, and to that end it is great.
Face value 00 85480 33583 1679 bond price pvcf 101815 2 duration years 4 university of illinois, urbana champaign fin 300 spring 2009. The present value equation for an annual coupon bond is given by. Bond duration and convexity simplified part 1 of 2. Thanks for contributing an answer to mathematics stack exchange. Convexity solutions blogs, comments and archive news on. We also show that the strongly monotonic assumption of the mapping may not need for the existence of solutions. 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. Understanding duration and convexity of fixed income.
In economics, nonconvexity refers to violations of the convexity assumptions of elementary economics. Proving that a specific function is quasiconvex mathoverflow. On the relation between the nonconvexity of a set and the nonconvexity of its. For a bond of face value usd1,000 with a semiannual coupon of 8. Pdf on the relation between the nonconvexity of a set. Stampacchia international school of mathematics of the e.
Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. Grc strategy risk and compliance software iconvexity. By using nonsmooth analysis knowledge, we provide the conditions for existence solutions of the variational inequalities problems in nonconvex setting. 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. The function structure is encapsulated using at most d over and underestimators. Globally solving nonconvex quadratic programming problems via.
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