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A new power option pricing method is designed for the financial market uncertainty that simultaneously involves randomness and fuzziness. The randomness in market uncertainty is modeled by a time\u2010fractional diffusion model, which describes trend memory in underlying asset prices. The fuzziness in market uncertainty is characterized by a triangular interval type\u20102 fuzzy numbers, which better captures the fuzziness of underlying asset prices. Considering the decision\u2010maker\u2019s subjective judgment, we show the price mean value with the possibility\u2010necessity weight and pessimistic\u2010optimistic index under the type\u20102 fuzzy environment. We develop the power option pricing model with the time\u2010fractional diffusion model and the triangular interval type\u20102 fuzzy numbers. Furthermore, the analytic solutions of pricing call power option and put power option are obtained and verified by the variational iterative reconstruction method. Our study shows that power option pricing, which adopts the time\u2010fractional model and the triangular interval type\u20102 fuzzy numbers, can better capture the trend memory and double fuzziness of the real market. In addition, a numerical example is provided to illustrate that the power option means the value is decreasing with respect to the pessimistic\u2010optimistic index and is fluctuating with respect to the possibility\u2010necessity weight index.<\/jats:p>","DOI":"10.1155\/2022\/5670482","type":"journal-article","created":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T17:20:09Z","timestamp":1664212809000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Power Option Pricing Based on Time\u2010Fractional Model and Triangular Interval Type\u20102 Fuzzy Numbers"],"prefix":"10.1155","volume":"2022","author":[{"given":"Tong","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5717-9396","authenticated-orcid":false,"given":"Pingping","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aimin","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,9,26]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1086\/260062"},{"key":"e_1_2_8_2_2","volume-title":"Mathematicl Modeling and Methods of Option Pricing","author":"Jiang L.","year":"2003"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2002.12.016"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2008.04.002"},{"key":"e_1_2_8_5_2","first-page":"51","article-title":"The fractional Black-Scholes equation","volume":"3","author":"Wyss W.","year":"2000","journal-title":"Fractional Calculus and Applied Analysis"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.07.053"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.05.015"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/621895"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40995-017-0244-7"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejbas.2014.10.003"},{"key":"e_1_2_8_11_2","first-page":"133","article-title":"Analytical solution of Black-Scholes model using fractional variational iteration","volume":"5","author":"Ahmad J.","year":"2013","journal-title":"International Journal of Modern Mathematical Sciences"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/194286"},{"key":"e_1_2_8_13_2","first-page":"1","article-title":"N-Fold compound option pricing with technical risk under fractional jump-diffusion model","volume":"11","author":"Zhao P. 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