4,296 research outputs found
Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization.
In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in [6, 7, 8].numerical scheme; stochastic optimal control; utility optimization; quadratic growth; distortion transformation; logarithmic transformation; BSPDE; BSDE;
Adaptive Submodular Influence Maximization with Myopic Feedback
This paper examines the problem of adaptive influence maximization in social
networks. As adaptive decision making is a time-critical task, a realistic
feedback model has been considered, called myopic. In this direction, we
propose the myopic adaptive greedy policy that is guaranteed to provide a (1 -
1/e)-approximation of the optimal policy under a variant of the independent
cascade diffusion model. This strategy maximizes an alternative utility
function that has been proven to be adaptive monotone and adaptive submodular.
The proposed utility function considers the cumulative number of active nodes
through the time, instead of the total number of the active nodes at the end of
the diffusion. Our empirical analysis on real-world social networks reveals the
benefits of the proposed myopic strategy, validating our theoretical results.Comment: Accepted by IEEE/ACM International Conference Advances in Social
Networks Analysis and Mining (ASONAM), 201
- …