Optimal investment and consumption problem for spread markets with stochastic volatility S. Albosaily, S. M. Pergamenshchikov
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ArticleContent type: Текст Media type: электронный Other title: Задача оптимального инвестирования и потребления для спредовых рынков состохастической волатильностью [Parallel title]Subject(s): спредовые финансовые рынки | стохастическая волатильность | Орнштейна-Уленбека процесс | стохастический подход | динамическое программирование | Гамильтона-Якоби-Беллмана уравнениеGenre/Form: статьи в сборниках Online resources: Click here to access online
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Международная научная конференция "Робастная статистика и финансовая математика – 2022" 04-05 июля 2022 г. : сборник статей С. 4-11Abstract: We consider a spread financial market defined by the Ornstein–Uhlenbeck (OU) process with a diffusion coefficient driven by a stochastic differential equation.For this market we study the optimal consumption/investment problem under logarithmic utilities. This problem is studied on the base of the stochastic dynamical programming approach.To this end we show aspecial verification theorem for this case.Then, we study the corresponding Hamilton–Jacobi–Bellman (HJB) equation and find its solution in explicit form.Finally,through this solution we construct the optimal financial strategies.
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We consider a spread financial market defined by the Ornstein–Uhlenbeck (OU) process with a diffusion coefficient driven by a stochastic differential equation.For this market we study the optimal consumption/investment problem under logarithmic utilities. This problem is studied on the base of the stochastic dynamical programming approach.To this end we show aspecial verification theorem for this case.Then, we study the corresponding Hamilton–Jacobi–Bellman (HJB) equation and find its solution in explicit form.Finally,through this solution we construct the optimal financial strategies.
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