Non-linear filtering and optimal investment under partial information for stochastic volatility models

Dalia Ibrahim () and Frédéric Abergel ()
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Dalia Ibrahim: FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec
Frédéric Abergel: FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec

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Abstract: This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled by a stochastic differential equations. Using the change of measure techniques, the partial observation context can be transformed into a full information context such that coefficients depend only on past history of observed prices (filter processes). Adapting the stochastic non-linear filtering, we show that under some assumptions on the model coefficients, the estimation of the filters depend on a priori models for the trend and the stochastic volatility. Moreover, these filters satisfy a stochastic partial differential equations named "Kushner-Stratonovich equations". Using the martingale duality approach in this partially observed incomplete model, we can characterize the value function and the optimal portfolio. The main result here is that the dual value function associated to the martingale approach can be expressed, via the dynamic programming approach, in terms of the solution to a semilinear partial differential equation which depends also on the filters estimate and the volatility. We illustrate our results with some examples of stochastic volatility models popular in the financial literature.

Keywords: Stochastic volatility; Non-linear filtering; Partial information; Martingale duality method; Semilinear partial differential equation; Utility maximization; Kushner-Stratonovich equations (search for similar items in EconPapers)
Date: 2018-06
New Economics Papers: this item is included in nep-gen, nep-ore and nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-01018869v5
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Published in Mathematical Methods of Operations Research, 2018, 87 (3), pp.311-346. ⟨10.1007/s00186-017-0609-x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01018869

DOI: 10.1007/s00186-017-0609-x

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