This paper proposes an item concept embedding (ICE) framework to model item concepts via textual information. Specifically, in the proposed framework there are two stages: graph construction and embedding learning. In the first stage, we propose a generalized network construction method to build a network involving heterogeneous nodes and a mixture of both homogeneous and heterogeneous relations. The second stage leverages the concept of neighborhood proximity to learn the embeddings of both items and words. With the proposed carefully designed ICE networks, the resulting embedding facilitates both homogeneous and heterogeneous retrieval, including item-to-item and word-to-item retrieval. Moreover, as a distributed embedding approach, the proposed ICE approach not only generates related retrieval results but also delivers more diverse results than traditional keyword-matching-based approaches. As our experiments on two real-world datasets show, ICE encodes useful textual information and thus outperforms traditional methods in various item classification and retrieval tasks.

Options can be priced by the lattice model, the results of which converge to the theoretical option value as the lattice’s number of time steps approaches infinity. The time complexity of a common dynamic programming pricing approach on the lattice is slow (at least ), and a large is required to obtain accurate option values. Although -time combinatorial pricing algorithms have been developed for the classical binomial lattice, significantly oscillating convergence behavior makes them impractical. The flexibility of trinomial lattices can be leveraged to reduce the oscillation, but there are as yet no linear-time algorithms on trinomial lattices. We develop -time combinatorial pricing algorithms for polynomial options that cannot be analytically priced. The commonly traded plain vanilla and power options are degenerated cases of polynomial options. Barrier options that cannot be stably priced by the binomial lattice can be stably priced by our -time algorithm on a trinomial lattice. Numerical experiments demonstrate the efficiency and accuracy of our -time trinomial lattice algorithms.