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Parametrización de BSVIEs profundos y aplicaciones basadas en aprendizaje

Nacira Agram1, Giulia Pucci1

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Este resumen es generado por máquina.

Este estudio introduce un nuevo método numérico para las ecuaciones integrales estocásticas inversas (BSVIEs), cruciales para la modelización financiera con memoria. El enfoque de aprendizaje profundo aproxima con precisión las soluciones para estas complejas ecuaciones y sus variantes reflejadas.

Palabras clave:
BSVIEsAprendizaje profundoSolucionadores de redes neuronalesRBSVIEsMedibilidad de Stricker-Yor

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Área de la Ciencia:

  • Análisis numérico
  • Procesos estocásticos
  • Aprendizaje automático en finanzas

Sus antecedentes:

  • Las ecuaciones integrales estocásticas inversas (BSVIEs) son esenciales para modelar escenarios financieros complejos como la inconsistencia temporal y las preferencias dependientes de la trayectoria.
  • Los métodos existentes tienen dificultades con la estructura temporal bidimensional y las dependencias intrincadas inherentes a las BSVIEs.

Objetivo del estudio:

  • Desarrollar un marco robusto de aproximación numérica para BSVIEs y sus extensiones reflejadas.
  • Establecer una base de bien planteamiento y medibilidad para BSVIEs en espacios de probabilidad producto.
  • Extender los solucionadores basados en aprendizaje profundo para ecuaciones diferenciales estocásticas inversas (BSDEs) al entorno de BSVIEs.

Principales métodos:

  • Se desarrolló un marco para el bien planteamiento y la medibilidad de BSVIEs utilizando una familia parametrizada de ecuaciones estocásticas inversas.
  • Se introdujo un esquema de aprendizaje de tiempo discreto que combina la discretización de Hamaguchi-Taguchi con redes neuronales profundas.
  • Se generalizaron las técnicas de solucionadores de BSDEs profundas para abordar la estructura temporal bidimensional de las BSVIEs.

Principales resultados:

  • Se estableció un análisis riguroso de convergencia para el esquema propuesto de aprendizaje profundo aplicado a BSVIEs.
  • Se extendió con éxito el solucionador numérico para manejar BSVIEs reflejadas, permitiendo aplicaciones en áreas como la utilidad recursiva retardada.
  • Se demostró la efectividad del método en la aproximación de soluciones para modelos financieros complejos.

Conclusiones:

  • El enfoque propuesto de aprendizaje profundo proporciona un método numérico eficaz y preciso para resolver BSVIEs y sus variantes reflejadas.
  • Este trabajo cierra la brecha entre los marcos teóricos de BSVIEs y las soluciones computacionales prácticas.
  • Los hallazgos tienen implicaciones significativas para las finanzas cuantitativas, particularmente en la modelización de utilidades recursivas y derivados financieros con efectos de memoria.