Volatility in U.S. Housing Sector and the REIT Equity Return

Alam, Mohammad Masud

doi:10.1007/s11146-022-09897-x

Cited by 4 publications

(1 citation statement)

References 118 publications

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“…As an alternative one can use a Monte Carlo scheme and this is the main idea of path integral control (Kappen, 2005;Theodorou, Buchli and Schaal, 2010;Theodorou, 2011;Morzfeld, 2015). Path integral control solves a class of stochastic control problems with a Monte Carlo method (Uddin et al, 2020;Islam, Alam and Afzal, 2021;Alam, 2021Alam, , 2022 for an HJB equation and this approach avoids the need for a global grid of the domain of the HJB equation (Yang et al, 2014). If the objective function is quadratic and the differential equations are linear, then the solution is given in terms of several Ricatti equations that can be solved efficiently (Kappen, 2007;Pramanik and Polansky, 2020b;Pramanik, 2021b;Pramanik and Polansky, 2021b).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Control of a SIR Model with Non-linear Incidence Rate Through Euclidean Path Integral

Pramanik¹

2022

Preprint

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This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a non-linear incidence rate to perform a detailed mathematical study of optimal lock-down intensity and vaccination rate under the COVID-19 pandemic environment. We use a Feynman-type path integral control approach to determine a Fokker-Plank type equation of this system. Since we assume the availability of information on the COVID-19 pandemic is complete and perfect, we can show a unique fixed point. A nonlinear incidence rate is used because, it can be raised from saturation effects that if the proportion of infected agents is very high so that exposure to the pandemic is inevitable, then the transmission rate responds slower than linearity to the increase in the number of infections. The simulation study shows that with higher diffusion coefficients susceptible and recovery curves keep the downward trends while the infection curve becomes ergodic. Finally, we perform a data analysis using UK data at the beginning of 2021 and compare it with our theoretical results.

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