A stochastic analog to Chebyshev centers and optimal average case algorithms

a benchmarking approach to optimal asset allocation for insurers and pension funds

uncertainty in the financial market will be driven by underlying brownian motions, while the assets are assumed to be general stochastic processes adapted to the filtration of the brownian motions. the goal of this study is to calculate the accumulated wealth in order to optimize the expected terminal value using a suitable utility function. this thesis introduced the lim-wong’s benchmark fun...

Optimal Stochastic Approximation Algorithms for Strongly Convex Stochastic Composite Optimization, II: Shrinking Procedures and Optimal Algorithms

In this paper we study new stochastic approximation (SA) type algorithms, namely, the accelerated SA (AC-SA), for solving strongly convex stochastic composite optimization (SCO) problems. Specifically, by introducing a domain shrinking procedure, we significantly improve the large-deviation results associated with the convergence rate of a nearly optimal AC-SA algorithm presented in [4]. Moreov...

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)

Broadcast and Gossip Stochastic Average Consensus Algorithms in Directed Topologies

We address the problem of a set of agents reaching consensus by computing the average of their initial states. We propose two randomized algorithms over a directed communication graph where either a random node broadcast its value or a randomly selected pair of nodes communicate in a distributed fashion. The proposed algorithms guarantee convergence in three important definitions, namely: almos...

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)