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Published in: Operations Research, vol. 50, no. 2
Publication year: 1999
Co-author 1: Graydon Barz

In this paper we present a method for valuing a power plant over a short-term period using Monte Carlo simulation. The power plant valuation problem is formulated as a multi-stage stochastic problem. We assume there are hourly markets for both electricity and the fuel used by the generator, and their prices follow some Ito processes. At each hour, the power plant operator must decide to run or not to run the unit so as to maximize expected pro t. A certain lead time for commitment decision is necessary to start up a unit. The commitment decision, once made, is subject to physical constraints such as minimum uptime and downtime constraints. The generator's startup cost is also taken into account in our model. In this paper, the Monte Carlo method is employed not only in forward-moving simulation, but also backward-moving recursion of dynamic programming. We demonstrate through numerical tests how the physical constraints a ect a power plant value.

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Published in: Energy Risk
Publication year: 2001
Co-author 1: Grace Lo
Co-author 2: Philip Mihlmester
Co-author 3: William Pepper
Co-author 4: William Hederman

Stochastic optimisation of energy asset portfolio and deployment decisions – increasing earnings while managing risk.

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Published in: Energy Risk
Publication year: 2001
Co-author 1: Nathan Collamer
Co-author 2: William Pepper

Following on from the article published in the October issue, here it is shown how the asset deployment model – which employs stochastic optimisation – holds certain advantages over other similar techniques

Keywords: optimal switching, Monte Carlo, Dynamic Programming, operational flexibility, impulse control, Snell envelope
Published in:
Publication year: 2005
Co-author 1: Michael Ludkovski

We consider the problem of optimal switching with finite horizon. This special case of stochastic impulse control naturally arises in the analysis of operational flexibility of exotic energy derivatives. The current practice relies on strips of European spark spread Call options that ignore the operational constraints of the asset. Instead, we propose a new approach based on recursive optimal stopping. Our model directly demonstrates that the optimal dispatch policies can be conveniently described with the aid of ‘switching boundaries’, similar to the free boundaries of standard American options. The thrust of our contribution is a new method of numerical solution based on Monte Carlo regressions. The scheme uses dynamic programming to simultaneously approximate the optimal switching times along all the simulated paths. Convergence analysis is carried out and numerical results are illustrated with a variety of concrete examples. We benchmark and compare our scheme to alternative numerical methods. As an aside, we also contribute to the numerical analysis of reflected backward stochastic differential equations and quasivariational inequalities.