Consumption and Investment Optimization under Constraints

We analyze a problem of maximization of expected terminal wealth and consumption under constraints in a general framework including financial models with constrained portfolios, labor income and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002). We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment and consumption plan to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999).Stochastic Optimization, Consumption and Investment Optimization, Duality Theory, Convex and State Constraints, Utility Maximization, Optional Decomposition, Minimax Theorem}

Investment Optimization under Constraints

We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some ``imperfection'', such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002), Long (2002). We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999).Stochastic Optimization, Investment Optimization, Duality Theory, Convex and State Constraints, Optional Decomposition

Utility Maximization in Imperfected Markets

We analyze a problem of maximization of expected terminal wealth and consumption in markets with some ``imperfection'', such as constraints on the permitted portfolios, labor income, or/and nonlinearity of portfolio dynamics. By using general optional decomposition under constraints in multiplicative form, we develop a dual formulation. Then, under some conditions imposed on the model setting and the utility functions, we are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem by convex duality.Stochastic Optimization, Utility Optimization, Duality Theory, Convex and State Constraints, Optional Decomposition, Optimal Stopping

On the nonlinear wave equation utt−B(t,‖u‖2,‖ux‖2)uxx=f(x,t,u,ux,ut,‖u‖2,‖ux‖2) associated with the mixed homogeneous conditions

AbstractIn this paper we consider the following nonlinear wave equation: (1)utt−B(t,‖u‖2,‖ux‖2)uxx=f(x,t,u,ux,ut,‖u‖2,‖ux‖2), x∈(0,1), 0<t<T,(2)ux(0,t)−h0u(0,t)=ux(1,t)+h1u(1,t)=0,(3)u(x,0)=u˜0(x), ut(x,0)=u˜1(x), where h0>0, h1⩾0 are given constants and B, f, u˜0, u˜1 are given functions. In Eq. (1), the nonlinear terms B(t,‖u‖2,‖ux‖2), f(x,t,u,ux,ut,‖u‖2,‖ux‖2) depend on the integrals ‖u‖2=∫Ω|u(x,t)|2dx and ‖ux‖2=∫01|ux(x,t)|2dx. In this paper I associate with problem (1)–(3) a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument. In case of B∈CN+1(R+3), B⩾b0>0, B1∈CN(R+3), B1⩾0, f∈CN+1([0,1]×R+×R3×R+2) and f1∈CN([0,1]×R+×R3×R+2) we obtain for the following equation utt−[B(t,‖u‖2,‖ux‖2)+ɛB1(t,‖u‖2,‖ux‖2)]uxx=f(x,t,u,ux,ut,‖u‖2,‖ux‖2)+ɛf1(x,t,u,ux,ut,‖u‖2,‖ux‖2) associated to (2), (3) a weak solution uɛ(x,t) having an asymptotic expansion of order N+1 in ɛ, for ɛ sufficiently small

Outage performance analysis of non-orthogonal multiple access with time-switching energy harvesting

In recent years, although non-orthogonal multiple access (NOMA) has shown its potentials thanks to its ability to enhance the performance of future wireless communication networks, a number of issues emerge related to the improvement of NOMA systems. In this work, we consider a half-duplex (HD) relaying cooperative NOMA network using decode-and-forward (DF) transmission mode with energy harvesting (Ell) capacity, where we assume the NOMA destination (D) is able to receive two data symbols in two continuous time slots which leads to the higher transmission rate than traditional relaying networks. To analyse EH, we deploy time-switching (TS) architecture to comprehensively study the optimal transmission time and outage performance at D. In particular, we are going to obtain closed-form expressions for outage probability (OP) with optimal TS ratio for both data symbols with both exact and approximate forms. The given simulation results show that the placement of the relay (R) plays an important role in the system performance.Web of Science253918

Optimal placement of battery energy storage system considering penetration of distributed generations

This paper proposes the optimal problem of location and power of the battery-energy-storage-system (BESS) on the distribution system (DS) considering different penetration levels of distributed generations (DGs). The objective is to minimize electricity cost of the DS in a typical day considering the power limit of DG fed to the DS. Growth optimizer (GO) is first applied to search the BESS’s location and power for each interval of the day. The considered problem and GO method are evaluated on the 18-node DS with two penetrations levels of photovoltaic system and wind turbine. The results demonstrate that the optimal BESS placement significantly reduces electricity cost. Furthermore, the optimal BESS location and power also help to reduce the cut capacity of DGs as their power greater than the load demand. The compared results between GO and particle swarm optimization (PSO) method have shown that GO reaches the better performance than PSO in term the optimal solution and the statistical results. Thus, GO is an effective approach for the BESS placement problem

Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t), u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I under a certain local Lipschitzian condition on f, a global existence and uniqueness theorem is proved. The proof is based on the paper [10] associated to a contraction mapping theorem and standard arguments of density. In Part} 2, under more restrictive conditions it is proved that the solution u(t) and its derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page

Energy harvesting based two-way full-duplex relaying network over a Rician fading environment: performance analysis

Full-duplex transmission is a promising technique to enhance the capacity of communication systems. In this paper, we propose and investigate the system performance of an energy harvesting based two-way full-duplex relaying network over a Rician fading environment. Firstly, we analyse and demonstrate the analytical expressions of the achievable throughput, outage probability, optimal time switching factor, and symbol error ratio of the proposed system. In the second step, the effect of various parameters of the system on its performance is presented and investigated. In the final step, the analytical results are also demonstrated by Monte Carlo simulation. The numerical results proved that the analytical results and the simulation results agreed with each other.Web of Science68112311