This paper studies the question of filtering and maximizing terminal wealthfrom expected utility in a partially information stochastic volatility models.The special features is that the only information available to the investor isthe one generated by the asset prices, and the unobservable processes will bemodeled by a stochastic differential equations. Using the change of measuretechniques, the partial observation context can be transformed into a fullinformation context such that coefficients depend only on past history ofobserved prices (filters processes). Adapting the stochastic non-linearfiltering, we show that under some assumptions on the model coefficients, theestimation of the filters depend on a priorimodels for the trend and thestochastic volatility. Moreover, these filters satisfy a stochastic partialdifferential equations named "Kushner-Stratonovich equations". Using themartingale duality approach in this partially observed incomplete model, we cancharacterize the value function and the optimal portfolio. The main result hereis that the dual value function associated to the martingale approach can beexpressed, via the dynamic programmingapproach, in terms of the solution to asemilinear partial differential equation. We illustrate our results with someexamples of stochastic volatility models popular in the financial literature.
展开▼
