{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:40:15Z","timestamp":1760125215401,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,18]],"date-time":"2023-03-18T00:00:00Z","timestamp":1679097600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The paper is dedicated to modeling electricity spot prices and pricing forward contracts on energy markets. The underlying dynamics of electricity spot prices is governed by a stochastic mean reverting diffusion with jumps having mixed-exponential distribution. Application of financial mathematics and stochastic methods enabled the derivation of the analytical formula for the forward contract\u2019s price in a crisp case. Since the model parameters\u2019 incertitude is considered, their fuzzy counterparts are introduced. Utilization of fuzzy arithmetic enabled deriving an analytical expression for the futures price and proposing a modified method for decision-making under uncertainty. Finally, numerical examples are analyzed to illustrate our pricing approach and the proposed financial decision-making method.<\/jats:p>","DOI":"10.3390\/e25030527","type":"journal-article","created":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T04:05:23Z","timestamp":1679285123000},"page":"527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Application of the Esscher Transform to Pricing Forward Contracts on Energy Markets in a Fuzzy Environment"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9325-4493","authenticated-orcid":false,"given":"Piotr","family":"Nowak","sequence":"first","affiliation":[{"name":"Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland"}]},{"given":"Micha\u0142","family":"Paw\u0142owski","sequence":"additional","affiliation":[{"name":"Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1287\/mnsc.1110.1393","article-title":"Option Pricing Under a Mixed-Exponential Jump Diffusion Model","volume":"57","author":"Cai","year":"2011","journal-title":"Manag. 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