Stochastic approach to model spot price and value forward contracts on energy markets under uncertainty

The paper deals with a model of electricity spot prices. The proposed dynamics of electricity spot prices is driven by a mean reverting diffusion with jumps having hyperexponential distribution. The analytical formula for the forward contract’s price is derived in a crisp case. Inasmuch as the model parameters are considered to be evaluated imprecisely, their fuzzy counterparts are introduced. With usage of the fuzzy arithmetic, the analytical expression for the forward contract’s price is derived. Several numerical examples highlighting attributes of the fuzzy forward electricity prices are brought out.

MIMICKING FINITE DIMENSIONAL MARGINALS OF A CONTROLLED DIFFUSION WITH JUMPS

Given a controlled diffusion with jumps, it is shown under some conditions that there exists a Markov controlled diffusion which has the same cost under any criterion which only depends on the one-dimensional distributions. This result is then used to prove that the finite dimensional marginal distribution of a controlled diffusion with jumps at a prescribed set of time instants can also be attained by using a control from a much smaller class of controls called "nearly Markov controls", extending the work of Borkar [4] to the discontinuous setting.