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

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

Multisource power splitting energy harvesting relaying network in half-duplex system over block Rayleigh fading channel: System performance analysis

Energy harvesting and information transferring simultaneously by radio frequency (RF) is considered as the novel solution for green-energy wireless communications. From that point of view, the system performance (SP) analysis of multisource power splitting (PS) energy harvesting (EH) relaying network (RN) over block Rayleigh-fading channels is presented and investigated. We investigate the system in both delay-tolerant transmission (DTT), and delay-limited transmission (DLT) modes and devices work in the half-duplex (HD) system. In this model system, the closed-form (CF) expressions for the outage probability (OP), system throughput (ST) in DLT mode and for ergodic capacity (EC) for DTT mode are analyzed and derived, respectively. Furthermore, CF expression for the symbol errors ratio (SER) is demonstrated. Then, the optimal PS factor is investigated. Finally, a Monte Carlo simulation is used for validating the analytical expressions concerning with all system parameters (SP).Web of Science81art. no. 6

On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical resultsComment: 20 page