{"id":"https://openalex.org/W4415083706","doi":"https://doi.org/10.1137/25m1743089","title":"Deep Learning for Energy Market Contracts: Dynkin Game with Doubly RBSDEs","display_name":"Deep Learning for Energy Market Contracts: Dynkin Game with Doubly RBSDEs","publication_year":2026,"publication_date":"2026-07-15","ids":{"openalex":"https://openalex.org/W4415083706","doi":"https://doi.org/10.1137/25m1743089"},"language":"en","primary_location":{"id":"doi:10.1137/25m1743089","doi":"https://doi.org/10.1137/25m1743089","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1743089","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-4","jufo-1","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2503.00880","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083592351","display_name":"Nacira Agram","orcid":"https://orcid.org/0000-0003-1662-0215","observed_orcids":["https://orcid.org/0000-0003-1662-0215"]},"institutions":[{"id":"https://openalex.org/I4405259960","display_name":"Digital Futures","ror":"https://ror.org/02ztymy03","country_code":"SE","type":"facility","lineage":["https://openalex.org/I161593684","https://openalex.org/I2800664555","https://openalex.org/I4405259960","https://openalex.org/I86987016"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Nacira Agram","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden, and Digital Futures, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-1662-0215","affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden, and Digital Futures, Sweden","institution_ids":["https://openalex.org/I4405259960","https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022818009","display_name":"Ihsan Arharas","orcid":"https://orcid.org/0000-0002-5922-7758","observed_orcids":["https://orcid.org/0000-0002-5922-7758"]},"institutions":[{"id":"https://openalex.org/I223464139","display_name":"Linnaeus University","ror":"https://ror.org/00j9qag85","country_code":"SE","type":"education","lineage":["https://openalex.org/I223464139"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ihsan Arharas","raw_affiliation_strings":["Department of Mathematics, Linnaeus University, V\u00e4xj\u00f6, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Linnaeus University, V\u00e4xj\u00f6, Sweden","institution_ids":["https://openalex.org/I223464139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099464033","display_name":"Giulia Pucci","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Giulia Pucci","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000644457","display_name":"Jan Rems","orcid":"https://orcid.org/0009-0007-1872-6669","observed_orcids":["https://orcid.org/0009-0007-1872-6669"]},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Jan Rems","raw_affiliation_strings":["Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7119,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95160603,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"17","issue":"3","first_page":"841","last_page":"876"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/contracts-for-difference","display_name":"contracts for difference","score":0.9129999876022339},{"id":"https://openalex.org/keywords/dynkin-games","display_name":"Dynkin games","score":0.8339999914169312},{"id":"https://openalex.org/keywords/optimal-stopping","display_name":"optimal stopping","score":0.7260000109672546},{"id":"https://openalex.org/keywords/deep-learning-for-pdes","display_name":"deep learning for PDEs","score":0.5979999899864197},{"id":"https://openalex.org/keywords/neural-network-approximation","display_name":"neural network approximation","score":0.6919999718666077},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.6299999952316284}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.786300003528595},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6635000109672546},{"id":"https://openalex.org/C99414536","wikidata":"https://www.wikidata.org/wiki/Q7098950","display_name":"Optimal stopping","level":2,"score":0.6366000175476074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5708000063896179},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5684000253677368},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5680000185966492},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4577000141143799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4287000000476837},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.40459999442100525},{"id":"https://openalex.org/C146733006","wikidata":"https://www.wikidata.org/wiki/Q676081","display_name":"Electricity market","level":3,"score":0.39169999957084656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.391400009393692},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C5465570","wikidata":"https://www.wikidata.org/wiki/Q5326898","display_name":"Early stopping","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2757999897003174},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2678999900817871},{"id":"https://openalex.org/C28761237","wikidata":"https://www.wikidata.org/wiki/Q7805321","display_name":"Time horizon","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C206658404","wikidata":"https://www.wikidata.org/wiki/Q12725","display_name":"Electricity","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C201236551","wikidata":"https://www.wikidata.org/wiki/Q7310809","display_name":"Relative value","level":2,"score":0.25220000743865967},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.250900000333786},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/25m1743089","doi":"https://doi.org/10.1137/25m1743089","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1743089","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-4","jufo-1","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2503.00880","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.00880","pdf_url":"https://arxiv.org/pdf/2503.00880","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2503.00880","doi":"https://doi.org/10.48550/arxiv.2503.00880","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2503.00880","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2503.00880","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.00880","pdf_url":"https://arxiv.org/pdf/2503.00880","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3524232687","display_name":"Advances in Stochastic Control Theory and Applications","funder_award_id":"2020-04697","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G8112547627","display_name":"Stochastic Methods with Applications","funder_award_id":"P1-0448","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415083706.pdf","grobid_xml":"https://content.openalex.org/works/W4415083706.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W573310676","https://openalex.org/W1676825492","https://openalex.org/W1865305834","https://openalex.org/W1969944159","https://openalex.org/W1972515188","https://openalex.org/W2008534422","https://openalex.org/W2020041898","https://openalex.org/W2022420776","https://openalex.org/W2050124602","https://openalex.org/W2061825652","https://openalex.org/W2093412621","https://openalex.org/W2115251869","https://openalex.org/W2119403614","https://openalex.org/W2164042878","https://openalex.org/W2167018969","https://openalex.org/W2738941123","https://openalex.org/W2993551995","https://openalex.org/W3047082415","https://openalex.org/W4297695336","https://openalex.org/W4387674034","https://openalex.org/W4389338953","https://openalex.org/W4393075043","https://openalex.org/W4394726698","https://openalex.org/W4399832505","https://openalex.org/W4406775409"],"related_works":["https://openalex.org/W4390722895","https://openalex.org/W3202809759","https://openalex.org/W634948115","https://openalex.org/W3124192252","https://openalex.org/W7172505534","https://openalex.org/W2566250548","https://openalex.org/W4307401865","https://openalex.org/W4393064308","https://openalex.org/W7161149618","https://openalex.org/W7165803816"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"formulate":[2],"a":[3,13,27,40,66,78,114,177,193,202,225],"Contract":[4],"for":[5],"Difference":[6],"(CfD)":[7],"with":[8,122],"early":[9,36],"exit":[10],"options":[11],"as":[12],"two-player":[14],"zero-sum":[15],"Dynkin":[16,196],"game,":[17],"capturing":[18],"the":[19,44,54,57,82,87,94,97,101,107,110,127,159,162,209,212,229,237],"strategic":[20],"interaction":[21,95],"between":[22,96,161],"an":[23],"electricity":[24,46,184],"producer":[25],"and":[26,39,56,100,145,165,201,224,232],"regulatory":[28],"authority.":[29],"The":[30,51,134,169,217],"payoff":[31],"structure":[32],"includes":[33],"running":[34],"revenues,":[35],"termination":[37],"penalties,":[38],"terminal":[41],"settlement,":[42],"while":[43],"underlying":[45],"prices":[47,185],"follow":[48],"mean-reverting":[49,183],"dynamics.":[50],"value":[52,98,231],"of":[53,81,109,126,211,228],"game":[55,197],"associated":[58],"feedback":[59],"optimal":[60,233],"stopping":[61,234],"rules":[62],"are":[63,91,205],"characterized":[64],"through":[65],"doubly":[67],"reflected":[68],"backward":[69,128],"stochastic":[70],"differential":[71],"equation":[72],"(DRBSDE).":[73],"In":[74,191],"addition,":[75,192],"we":[76,112],"provide":[77],"structural":[79],"characterization":[80],"reflection":[83],"mechanism,":[84],"showing":[85],"how":[86],"cumulative":[88],"penalty":[89],"processes":[90],"generated":[92],"by":[93,181],"process":[99],"time":[102,120,142],"dependent":[103,143],"barriers.":[104],"To":[105],"approximate":[106],"solution":[108],"DRBSDE,":[111],"propose":[113],"learning-based":[115],"numerical":[116,167,218],"method":[117],"that":[118],"combines":[119],"discretization":[121],"neural":[123],"network":[124],"approximations":[125],"components":[129],"along":[130],"simulated":[131],"price":[132],"trajectories.":[133],"approach":[135],"avoids":[136],"explicit":[137],"state":[138],"space":[139],"discretization,":[140],"accommodates":[141],"barriers,":[144],"is":[146,155,174],"applicable":[147],"in":[148,198,214],"moderately":[149],"high-dimensional":[150],"settings.":[151,216],"A":[152],"convergence":[153],"result":[154],"established":[156],"to":[157,207],"justify":[158],"link":[160],"continuous-time":[163],"formulation":[164],"its":[166],"approximation.":[168],"proposed":[170],"Deep":[171],"DRBSDE":[172],"solver":[173,213],"illustrated":[175],"on":[176],"CfD":[178],"model":[179],"driven":[180],"24-dimensional":[182],"representing":[186],"multiple":[187],"European":[188],"market":[189],"zones.":[190],"symmetric":[194],"benchmark":[195],"dimension":[199],"20":[200],"mean-field":[203],"extension":[204],"considered":[206,238],"assess":[208],"validity":[210],"controlled":[215],"results":[219],"demonstrate":[220],"stable":[221],"training":[222],"behavior":[223],"consistent":[226],"approximation":[227],"contract":[230],"regions":[235],"across":[236],"examples.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-12T00:00:00"}