## Abstract

This paper presents a real option valuation model of a power plant, which accounts for physical constraints and market incompleteness. Switching costs, minimum on-off times, ramp rates, or non-constant heat rates are important characteristics that can lead, if neglected, to overestimated values. The existence of non-hedgeable uncertainties is also a feature of energy markets that can impact assets value. We use the utility indifference approach to define the value of the physical asset. We derive the associated mixed optimal switching-control problem and provide a characterization of its solution by means of a coupled system of reflected Backward Stochastic Differential Equations (BSDE). We relate this system to a system of variational inequalities, and we provide a numerical comparative study by implementing BSDE simulation algorithms, and PDE finite differences schemes.

Original language | English (US) |
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Pages (from-to) | 47-75 |

Number of pages | 29 |

Journal | Mathematical Methods of Operations Research |

Volume | 70 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2009 |

## Keywords

- Backward stochastic differential equation
- Finite differences for PDE
- Non-linear Monte Carlo methods
- Real option
- Utility indifference

## ASJC Scopus subject areas

- Software
- Mathematics(all)
- Management Science and Operations Research