Martingale Approach To Optimal Portfolio-Consumption Problems In Markov-Modulated Pure-Jump Models

Título traducido de la contribución: Enfoque de Martingale a los problemas óptimos de consumo de cartera en modelos de salto puro modulados por Markov

rafael serrano, Oscar López

Resultado de la investigación: Contribución a RevistaArtículo

Resumen

Estudiamos estrategias de inversión óptimas que maximizan la utilidad esperada del consumo y la riqueza de los terminales en un modelo de precios de activos de salto puro con distribuciones de tamaño de salto moduladas por Markov (cambio de régimen). Damos las condiciones suficientes para la existencia de políticas óptimas y encontramos expresiones de forma cerrada para la función de valor óptima para agentes con utilidad de poder logarítmico y fraccionario (CRRA) en el caso de cadenas Markov de dos estados. Las principales herramientas son las técnicas de dualidad convexa, el cálculo estocástico para procesos de salto puro y las fórmulas explícitas para los momentos de los procesos telegráficos con saltos aleatorios modulados por Markov.
Idioma originalEnglish (US)
Páginas (desde-hasta)261 - 291
PublicaciónStochastic Models
Volumen31
DOI
EstadoPublished - 2015

Huella dactilar

Telegraph
Optimal Portfolio
Martingale
Markov processes
Jump
Convex Duality
Optimal Value Function
Regime Switching
Stochastic Calculus
Optimal Investment
Jump Process
Fractional Powers
Expected Utility
Optimal Policy
Explicit Formula
Markov chain
Logarithmic
Closed-form
Maximise
Model

Citar esto

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title = "Martingale Approach To Optimal Portfolio-Consumption Problems In Markov-Modulated Pure-Jump Models",
abstract = "We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for existence of optimal policies and find closed-form expressions for the optimal value function for agents with logarithmic and fractional power (CRRA) utility in the case of two-state Markov chains. The main tools are convex duality techniques, stochastic calculus for pure-jump processes, and explicit formulae for the moments of telegraph processes with Markov-modulated random jumps.",
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Martingale Approach To Optimal Portfolio-Consumption Problems In Markov-Modulated Pure-Jump Models. / serrano, rafael; López, Oscar.

En: Stochastic Models, Vol. 31, 2015, p. 261 - 291.

Resultado de la investigación: Contribución a RevistaArtículo

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AU - serrano, rafael

AU - López, Oscar

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AB - We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for existence of optimal policies and find closed-form expressions for the optimal value function for agents with logarithmic and fractional power (CRRA) utility in the case of two-state Markov chains. The main tools are convex duality techniques, stochastic calculus for pure-jump processes, and explicit formulae for the moments of telegraph processes with Markov-modulated random jumps.

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DO - 10.1080/15326349.2014.999286

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