A Markov decision problem in a risk model with interest rate and Markovian environment

Periodic strategies in optimal execution with multiplicative price impact

“…Bertsimas and Lo () also made fundamental contributions considering a discrete random walk model. In our case, the strategies are described as Lebesgue–Stieltjes integrals with respect to the paths of the Poisson process, called periodic strategies , in analogy with the terminology used in insurance models when dividend payment decisions are taken; see, for instance, Avanzi, Cheung, Wong, and Woo (); Avanzi, Tu, and Wong (); Tan, Yang, Li, and Cheng (); and Pérez and Yamazaki ().…”

“…In contrast with the multiplicative impact model presented here, in the seminal papers of Almgren and Chriss [4], [5] and Almgren [3], the execution strategies are assumed to be absolutely continuous functions of time, having a price impact acting in an additive way; Bertsimas and Lo [11] also made fundamental contributions considering a discrete random walk model. In our case the strategies are described as Lebegue-Stieltjes integrals with respect to the paths of the Poisson process, named periodic strategies, in analogy with the terminology used in insurance models when dividend payment decisions are taken; see, for instance, [7,8,30,31].…”