We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. The corresponding game is an example of an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for … Read more
Computing semiparametric bounds for option prices is a widely studied pricing technique. In contrast to parametric pricing techniques, such as Monte-Carlo simulations, semiparametric pricing techniques do not re- quire strong assumptions about the underlying asset price distribution. We extend classical results in this area in two main directions. First, we derive closed-form semiparametric bounds for … Read more
In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and \”{Ozevin} \cite{MO04a,MO04b} and Zhao \cite{GZ01}, however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs … Read more
We present a new methodology for the numerical pricing of a class of exotic derivatives such as Asian or barrier options when the underlying asset price dynamics are modelled by a geometric Brownian motion or a number of mean-reverting processes of interest. This methodology identifies derivative prices with infinite-dimensional linear programming problems involving the moments … Read more
We propose a unified theory that links uncertainty sets in robust optimization to risk measures in portfolio optimization. We illustrate the correspondence between uncertainty sets and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these measures. We also show that by using properly defined … Read more
Non-Linear Stochastic Fractional programming models provide numerous insights into a wide variety of areas such as in financial derivatives. Portfolio optimization has been one of the important research fields in modern finance. The most important character within this optimization problem is the uncertainty of the future returns on assets. The objective of this study is … Read more
In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval … Read more
We present a method to compute the implied volatility of American options as a mathematical program with equilibrium constraints. The formulation we present is new, as are the convergence results we prove. The algorithm holds the promise of being practical to implement, and we demonstrate some preliminary numerical results to this end. CitationPrinceton University working … Read more
The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which convex transaction costs are incurred to rebalance an investment portfolio. In particular, we consider linear, piecewise linear, and quadratic transaction costs. The Markowitz framework of mean-variance efficiency … 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