{"id":"W77275776","doi":"10.1007/978-3-642-17254-0_18","title":"Numerical Methods for Nonlinear PDEs in Finance","year":2011,"lang":"en","type":"book-chapter","venue":"","topic":"Stochastic processes and financial applications","field":"Economics, Econometrics and Finance","cited_by":42,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Viscosity solution; Discretization; Hamilton–Jacobi–Bellman equation; Nonlinear system; Partial differential equation; Convergence (economics); Mathematics; Applied mathematics; Viscosity; Numerical analysis; Volatility (finance); Mathematical optimization; Mathematical analysis; Economics; Bellman equation; Econometrics; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008968778,0.001109432,0.001176816,0.0009792042,0.0003736504,0.001368338,0.00115574,0.001690736,0.009959303],"category_scores_gemma":[0.003228399,0.0005105467,0.0006937939,0.00129333,0.00142244,0.001661049,0.001273521,0.002683259,0.004795863],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006800107,"about_ca_system_score_gemma":0.0007232139,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001563699,"about_ca_topic_score_gemma":0.002285548,"domain_scores_codex":[0.9994988,0.0001379483,0.00003278898,0.00005589894,0.0002555264,0.00001891452],"domain_scores_gemma":[0.9991269,0.0005380447,0.00003400778,0.00009649131,0.0001736165,0.00003084718],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003286739,0.00007145362,0.0002845603,0.0007816748,0.00006618054,0.00008458948,0.000192116,0.06868077,0.00334517,0.5379518,0.06955942,0.3189494],"study_design_scores_gemma":[0.00002889036,0.00001789379,0.0002789358,0.0002232293,0.0000209916,0.0001360889,0.00003326815,0.3255924,0.001259162,0.5166913,0.1556856,0.00003199519],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.001425328,0.02898651,0.9307631,0.001201537,0.001550196,0.00004027885,0.0001643133,0.0006132575,0.03525549],"genre_scores_gemma":[0.05960402,0.03231718,0.7670444,0.000820541,0.002651015,0.0004014148,0.0008569229,0.001390219,0.1349143],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.009959303,"threshold_uncertainty_score":0.03331721,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07337220975199756,"score_gpt":0.2989276278460629,"score_spread":0.2255554180940653,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}