Properties of Large Deviations of Empirical Estimates in a Stochastic Optimization Problem for a Homogeneous Random Field

2020 ◽  
Vol 52 (12) ◽  
pp. 12-25
Author(s):  
Pavel S. Knopov ◽  
Evgeniya J. Kasitskaya
Keyword(s):  
Large Deviations ◽  
Stochastic Optimization ◽  
Random Field ◽  
Optimization Problem ◽  
Homogeneous Random Field ◽  
Empirical Estimates ◽  
Stochastic Optimization Problem

scholarly journals Optimizing Green Computing Awareness for Environmental Sustainability and Economic Security as a Stochastic Optimization Problem

2017 ◽  
Vol 9 (10) ◽  
pp. 1857 ◽  
Author(s):  
Emmanuel Okewu ◽  
Sanjay Misra ◽  
Rytis Maskeliūnas ◽  
Robertas Damaševičius ◽  
Luis Fernandez-Sanz
Keyword(s):  
Stochastic Optimization ◽  
Environmental Sustainability ◽  
Optimization Problem ◽  
Economic Security ◽  
Green Computing ◽  
Stochastic Optimization Problem

scholarly journals Risk-Based Two-Stage Stochastic Optimization Problem of Micro-Grid Operation with Renewables and Incentive-Based Demand Response Programs

Energies ◽  
2018 ◽  
Vol 11 (3) ◽  
pp. 610 ◽  
Author(s):  
Pouria Sheikhahmadi ◽  
Ramyar Mafakheri ◽  
Salah Bahramara ◽  
Maziar Damavandi ◽  
João Catalão
Keyword(s):  
Stochastic Optimization ◽  
Demand Response ◽  
Optimization Problem ◽  
Two Stage ◽  
Stochastic Optimization Problem ◽  
Micro Grid ◽  
Grid Operation ◽  
Demand Response Programs

scholarly journals Value functions in a regime switching jump diffusion with delay market model

2021 ◽  
Vol 6 (10) ◽  
pp. 11595-11609
Author(s):  
Dennis Llemit ◽  
◽  
Jose Maria Escaner IV
Keyword(s):  
Differential Equation ◽  
Stochastic Optimization ◽  
Utility Function ◽  
Optimization Problem ◽  
Jump Diffusion ◽  
Risky Asset ◽  
Market Model ◽  
Logarithmic Utility ◽  
Stochastic Optimization Problem ◽  
History Of

<abstract><p>In this paper, we consider a market model where the risky asset is a jump diffusion whose drift, volatility and jump coefficients are influenced by market regimes and history of the asset itself. Since the trajectory of the risky asset is discontinuous, we modify the delay variable so that it remains defined in this discontinuous setting. Instead of the actual path history of the risky asset, we consider the continuous approximation of its trajectory. With this modification, the delay variable, which is a sliding average of past values of the risky asset, no longer breaks down. We then use the resulting stochastic process in formulating the state variable of a portfolio optimization problem. In this formulation, we obtain the dynamic programming principle and Hamilton Jacobi Bellman equation. We also provide a verification theorem to guarantee the optimal solution of the corresponding stochastic optimization problem. We solve the resulting finite time horizon control problem and show that close form solutions of the stochastic optimization problem exist for the cases of power and logarithmic utility functions. In particular, we show that the HJB equation for the power utility function is a first order linear partial differential equation while that of the logarithmic utility function is a linear ordinary differential equation.</p></abstract>

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