Functional Stochastic Analysis and Applications

• Grant number: 17/23003-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Francys Andrews de Souza
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications, AP.TEM

Abstract

We will characterize the epsilon-controls for pairs trade strategies driven by Fractional Brownian motion. To do this, we will use the pathwise analysis and a discretization structure proposed by Leão and Ohashi (2013) together with measurable selection arguments obtained in the article Leão, Ohashi e Souza(2017). With these objects, we will be able to characterize the epsilon-optimal controls for this type of strategy, and then we will be able to analyse the behavior of the strategy (profitability/loss) in a simulation structure.In addition, we will present a concrete methodology for calculating to epsilon-optimal controls for non-Markovian systems with partial observations, this part is a continuation and expansion of the theory developed in Leão, Ohashi e Souza(2017). Finally, after we have finished developing the theory for partial observations, we will work again on the strategy of Pairs Trade, but now on the case of partial observations. The central idea is to find a epsilon-optimal predictable control in the filtering generated by what the observable part. In this context, we will assume that asset volatility is not observed,and that we are able to observe is only the price.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LIMA, LOURIVAL; RUFFINO, PAULO; SOUZA, FRANCYS. Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications. European Physical Journal-Special Topics, JUN 2021. (15/50122-0, 17/23003-6, 20/04426-6)

OHASHI, ALBERTO; DE SOUZA, FRANCYS A.. L-p uniform random walk-type approximation for Fractional Brownian motion with Hurst exponent 0 < H < 1/2. Electronic Communications in Probability, v. 25, 2020. (17/23003-6)

LIMA, LOURIVAL; RUFFINO, PAULO; SOUZA, FRANCYS. Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications. European Physical Journal-Special Topics, v. 230, n. 14-15, p. 2783-2792, OCT 2021. (17/23003-6, 20/04426-6, 15/50122-0)

OHASHI, ALBERTO; DE SOUZA, FRANCYS A.. L^p uniform random walk-type approximation for Fractional Brownian motion with Hurst exponent 0 < H < 1/2. Electronic Communications in Probability, v. 25, p. 13-pg., 2020-01-01. (17/23003-6)