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In this paper we study an optimal portfolio selection problem under instantaneous price impact. Based on some empirical analysis in the literature, we model such impact as a concave function of the trading size when the trading size is small. The price impact can be thought of as either a...
We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing...
We consider a differential system of neutral type with distributed delay. We obtain a precise norm estimation of semigroup generated by the operator corresponding to the system in question. Our result is based on a spectral analysis of the operator and some uniform estimation of norms of the...
We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain D . We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the normal to the boundary and an interior condition weaker than...
Via Carleman’s estimates we prove uniqueness and continuous dependence results for the temporal traces of solutions to overdetermined linear ill-posed problems related to Schrödinger and plate equation. The overdetermination is prescribed in an open subset of the (space-time) lateral boundary.
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