Reha H. Tütüncü The risk parity optimization problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization approach and the equal weighting approach. In this paper, we discuss the problem of finding portfolios … Read more
This software is designed to solve primal and dual semidefinite-quadratic-linear conic programming problems (known as SQLP problems) whose constraint cone is a product of semidefinite cones, second-order cones, nonnegative orthants and Euclidean spaces, and whose objective function is the sum of linear functions and log-barrier terms associated with the constraint cones. This includes the special … Read more
Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating the evolution of the risk-neutral density in time. Our method uses bicubic splines … Read more
We propose a primal-dual path-following Mehrotra-type predictor-corrector method for solving convex quadratic semidefinite programming (QSDP) problems. For the special case when the quadratic term has the form $\frac{1}{2} X \bul (UXU)$, we compute the search direction at each iteration from the Schur complement equation. We are able to solve the Schur complement equation efficiently via … Read more
We study multi-period nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty, we show that quasi-convexity of the optimal value function of certain subproblems is sufficient for the reducibility of the resulting robust optimization … Read more
For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single and multiple period settings. We show that the problem of finding the “most robust” profit opportunity can be solved as a convex quadratic programming problem, and investigate its relation to the Sharpe … Read more
We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and … Read more
This article considers continuous trajectories of the vector fields induced by primal-dual potential-reduction algorithms for solving linear programming problems. It is known that these trajectories converge to the analytic center of the primal-dual optimal face. We establish that this convergence may be tangential to the central path, tangential to the optimal face, or in between, … Read more
This article considers continuous trajectories of the vector fields induced by two different primal-dual potential-reduction algorithms for solving linear programming problems. For both algorithms, it is shown that the associated continuous trajectories include the central path and the duality gap converges to zero along all these trajectories. For the algorithm of Kojima, Mizuno, and Yoshise, … Read more
This software package is a MATLAB implementation of infeasible path-following algorithms for solving conic programming problems whose constraint cone is a product of semidefinite cones, second-order cones, and/or nonnegative orthants. It employs a predictor-corrector primal-dual path-following method, with either the HKM or the NT search direction. The basic code is written in Matlab, but key … Read more