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In this paper we introduce a jump-diffusion model of shot-noise type for stock prices, taking into account over and under-reaction of the market to incoming news. We work in a partial information setting, by supposing that standard investors do not have access to the market direction, the drift, (modeled via a random variable) after a jump. We focus on the expected (logarithmic) utility maximization problem by providing the optimal investment strategy in explicit form, both under full (i.e., from the insider point of view, aware of the right kind of market reaction at any time) and under partial information (i.e., from the standard investor viewpoint, who needs to infer the kind of market reaction from data). We test our results on market data relative to Enron and Ahold. The three main contributions of this paper are: the introduction of a new market model dealing with over and under-reaction to news, the explicit computation of the optimal filter dynamics using an original approach combining enlargement of filtrations with Innovation Theory and the application of the optimal portfolio allocation rule to market data

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This paper concerns with numerical resolution of an impulse control problem under state constraints arising from optimal portfolio selection under liquidity risk and price impact. We show that the value function could be obtained as the limit of an iterative procedure where each step is an optimal stopping problem and the reward function is related to the impulse operator. Given the dimension of our problem and the complexity of its solvency region, we use a numerical approximation algorithm based on quantization procedure instead of finite difference methods to calculate the value function, the transaction and no-transaction regions. We also focus on the convergence of our numerical scheme, in particular, we show that it satisfies monotonicity, stability and consistency properties. We further enrich our studies with some numerical results for the optimal transaction strategy. B Mohamed Mnif mohamed.mnif@enit.rnu.tn M'hamed Gaigi