Browsing by Author "Krawczyk, Jacek B"

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Open Access
Approximations to viability kernels for sustainable macroeconomic policies
(Te Herenga Waka—Victoria University of Wellington, 2011) Krawczyk, Jacek B; Pharo, Alastair; Simpson, Mark
Maintaining an open economy within certain bounds on inflation, output gap and exchange rate can help sustainable economic development. Macroeconomics proposes monetary-policy models that describe evolution of the above quantities. We use one such model, constituted by a four-metastate one-control system, to compute viability kernel approximations that one can use to assist the central bank to establish "sustainable" policies. We propose a simple heuristic algorithm that leads to kernel approximations for this and similar models.
Open Access
Basic understanding of social inequality dynamics
(Te Herenga Waka—Victoria University of Wellington, 2015) Krawczyk, Jacek B; Townsend, Wilbur
We provide an introduction to a model of social inequality dynamics. Because capital is distributed less equally than labour, we propose that that one of the main forces driving income inequality is the ratio of factor shares. In this paper we give an easy proof to show that this ratio is driven by the output elasticity of capital.
Restricted
Electricity Market Games with Constraints on Transmission Capacity and Emissions
(Te Herenga Waka—Victoria University of Wellington, 2007) Zuccollo, James; Contreras, Javier; Krawczyk, Jacek B
Consider an electricity market populated by competitive agents using thermal generating units. Such generation involves the emission of pollutants, on which a regulator might impose constraints. Transmission capacities for sending energy may naturally be restricted by the grid facilities. Both pollution standards and transmission capacities can impose several constraints upon the joint strategy space of the agents. We propose a coupled constraints equilibrium as a solution to the regulator's problem of avoiding both congestion and excessive pollution. Using the coupled constraints Lagrange multipliers as taxation coefficients the regulator can compel the agents to obey the multiple constraints. However, for this modification of the players' payoffs to induce the required behaviour a coupled constraints equilibrium needs to exist and be unique. A three-node bilateral market example with a DC model of the transmission line constraints described in possesses these properties and will be used in this paper to discuss and explain the behaviour agents subjected to coupled constraints.
Open Access
InfSOCSol2: an Updated MATLAB (R) Package For Approximating the Solution to a Continuous-Time Infinite Horizon Stochastic Optimal Control Problem
(Te Herenga Waka—Victoria University of Wellington, 2008) Azzato, Jeffrey; Krawczyk, Jacek B
This paper describes a suite of MATLAB (R) routines devised to provide an approximately optimal solution to an infinite-horizon stochastic optimal control problem. The suite is an updated version of that described in [Kra01b]. Its routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [Kra01c]
Open Access
InfsocSol3: An updated MATLAB® package for approximating the solution to a continuous-time infinite horizon stochastic optimal control problem
(Te Herenga Waka—Victoria University of Wellington, 2014) Krawczyk, Jacek B; Pharo, Alastair S
This paper describes a suite of MATLAB® routines devised to provide an approximately optimal solution to an infinite-horizon stochastic optimal control problem. The suite is an updated version of that described in [1] and [2]. Its routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [3].
Open Access
The Invisible Polluter: Can Regulators Save Consumer Surplus?
(Te Herenga Waka—Victoria University of Wellington, 2008) Krawczyk, Jacek B; Zuccollo, James; Contreras, Javier
Consider an electricity market populated by competitive agents using thermal generating units. Such generation involves the emission of pollutants, on which a regulator might impose constraints. Transmission capacities for sending energy may naturally be restricted by the grid facilities. Both pollution standards and transmission capacities can impose several constraints upon the joint strategy space of the agents. We propose a coupled constraints equilibrium as a solution to the regulator's problem of avoiding both congestion and excessive pollution. Using the coupled constraints' Lagrange multipliers as taxation coefficients the regulator can compel the agents to obey the multiple constraints. However, for this modification of the players' payoffs to induce the required behaviour a coupled constraints equilibrium needs to exist and must also be unique. A three-node market example with a dc model of the transmission line constraints described in [8] and [2] possesses these properties. We extend it here to utilise a two-period load duration curve and, in result, obtain a two-period game. The implications of the game solutions obtained for several weights, which the regulator can use to vary the level of generators' responsibilities for the constraints' satisfaction, for consumer and producer surpluses will be discussed.
Open Access
Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems
(Te Herenga Waka—Victoria University of Wellington, 2014) Krawczyk, Jacek B; Pharo, Alastair S
This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control. This document details version 2.0 of the software.
Open Access
New Zealand inequality and the struggle between capital and labour
(Te Herenga Waka—Victoria University of Wellington, 2015) Krawczyk, Jacek B; Townsend, Wilbur
This paper examines whether changes in New Zealand income inequality can be attributed to the shares of national income taken by capital and labour. Data on income inequality aggregates both capital income (rents, interest, profits) and labour income (wages and salaries). It is possible that changes in inequality correspond only to changes within the distributions of capital income and labour income, and that a rhetoric which emphasises the struggle between capital and labour is misguided. We find this is not the case: both an econometric analysis of income shares and a historical analysis of major policies demonstrates that the struggle between capital and labour matters.
Restricted
NIRA-GUI: A matlab application which solves for couple-constraint nash equibria from a symbolic specification
(Te Herenga Waka—Victoria University of Wellington, 2014) Krawczyk, Jacek B; Townsend, Wilbur
A powerful method for computing Nash equilibria in constrained, multi-player games is created when the relaxation algorithm and the Nikaido-Isoda function are used within a MATLAB application. This paper describes that application, which is able to solve static and open-loop dynamic games specifed symbolically.
Open Access
On loss-avoiding lump-sum pension optimization with contingent targets
(Te Herenga Waka—Victoria University of Wellington, 2011) Azzato, Jeffrey; Krawczyk, Jacek B; Sissons, Christopher
Consider a lump-sum pension fund problem, in which an agent deposits an amount with a fund manager up front and is later repaid a lump sum x(T) after time T. The fund manager may be both cautious in seeking a payoff x(T) meeting a certain target, but relaxed toward the possibility of exceeding this target. We use a computational method in stochastic optimal control (“SOCSol”) to find approximately-optimal decision rules for such “cautious-relaxed” fund managers. In particular, we examine fund optimisation problems in which the target is contingent upon market conditions such as inflation.
Open Access
Parallel SOCSol: a Parallel MATLAB (R) Package For Approximating the Solution to a Continuous-Time Stochastic Optimal Control Problem
(Te Herenga Waka—Victoria University of Wellington, 2008) Azzato, Jeffrey D; Krawczyk, Jacek B; Original Collection id - http://researcharchive.vuw.ac.nz/handle/10063/385; Original Collection Name - School of Economics and Finance · Te Kura Ohaoha Pūtea
This article is a modified version of [AK06]. Both articles explain how a suite of MATLAB (R) routines distributed under the generic name SOCSol can be used to obtain optimal solutions to continuous-time stochastic optimal control problems. The difference between the SOCSol suites described by the articles arises from the underlying computing platforms used. This article describes a beta version of SOCSol that utilises the MATLAB (R) Parallel Computing Toolbox (TM), while [AK06] describes a version of SOCSol that does not use parallel computing methods.
Open Access
A Report on NISOCSol: an Algorithm For Approximating Markovian Equlibria in Dynamic Games with Coupled-Constraints
(Te Herenga Waka—Victoria University of Wellington, 2006) Krawczyk, Jacek B; Azzato, Jeffrey D
In this report, we outline a method for approximating a Markovian (or feedback-Nash) equilibrium of a dynamic game, possibly subject to coupled-constraints. We treat such a game as a "multiple" optimal control problem. A method for approximating a solution to a given optimal control problem via backward induction on Markov chains was developed in [Kra01]. A Markovian equilibrium may be obtained numerically by adapting this backward induction approach to a stage Nikaido-Isoda function (described in [KZ06]).
Open Access
A Report on Using Parallel MATLAB (R) For Solutions to Stochastic Optimal Control Problems
(Te Herenga Waka—Victoria University of Wellington, 2008) Azzato, Jeffrey D; Krawczyk, Jacek B
Parallel MATLAB (R) is a recent MathWorks (TM) product enabling the use of parallel computing methods on multicore personal computers. SOCSol is the generic name of a suite of MATLAB (R) routines that can be used to obtain optimal solutions to continuous-time stochastic optimal control problems. In this report, we compare the performance of a new version of SOCSol utilising parallel MATLAB (R) with that of another version not using parallel computing methods.
Open Access
Sensitivity of cautious-relaxed investment policies to target variation
(Te Herenga Waka—Victoria University of Wellington, 2013) Foster, Jarred; Krawczyk, Jacek B
This study builds on recent findings that target-based utility measures, used in the dynamic portfolio optimisation, deliver investment policies that can generate leftskewed payoff distributions. These policies can lead to small probabilities of low payoffs. This is in contrast to the classical portfolio optimisation strategies that commonly deliver right-skewed payoff distributions, which imply a high probability of losses. The left-skewed payoff distributions can be obtained when a “cautious-relaxed” investment policy is applied in portfolio management. Such a policy will be adopted by investors who are both cautious in seeking a payoff meeting a certain target, but relaxed toward the possibility of exceeding it. We use computational methods to analyse the effects of varying the target on the payoff distribution and also examine how the fund manager’s explicit preferences, when they differ from the investor’s, can impact the distribution. We found that increasing the target causes the distribution to become less left skewed. Lowering the target slightly, keeps the left-skewed payoff distribution albeit the mode diminishes. Decreasing the target substantially so it is below the safe investment payoff, changes the skew. Investor’s payoff will not suffer even if the actual fund manager allows for their own utility in the optimisation problem.
Open Access
SOCSol4L: an Improved MATLAB (R) Package For Approximating the Solution to a Continuous-Time Stochastic Optimal Control Problem
(Te Herenga Waka—Victoria University of Wellington, 2006) Azzato, Jeffrey D; Krawczyk, Jacek B
Computing the solution to a stochastic optimal control problem is difficult. A method of approximating a solution to a given continuous-time stochastic optimal control problem using Markov chains was developed in [Kra01]. This paper describes a suite of MATLAB (R) routines implementing this method.
Open Access
Viability of an economy with constrained inequality
(Te Herenga Waka—Victoria University of Wellington, 2015) Krawczyk, Jacek B; Townsend, Wilbur
Governments want to prevent high inequality while maintaining economic effi ciency. This paper investigates how an economy can satisfy both these constraints. We use the relative factor share as a proxy for inequality and so can use a representative agent model to understand how inequality evolves. Our representative agent model includes capital, consumption and debt which, like the relative factor share, are influenced by tax rates. Whether the model's evolutions can be constrained is understood as a problem of viability theory, and so we compute the viability kernels corresponding to our constraints. These kernels explain both how policy makers should act and why they act as they currently do. For example, we show that substantial government debt will require policy makers to reduce inequality. More importantly, we demonstrate that viability theory is a meaningful, interesting approach to understanding the tradeoff between inequality and efficiency.