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

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}

Optimal Investment in the Development of Oil and Gas Field

Let an oil and gas field consists of clusters in each of which an investor can launch at most one project. During the implementation of a particular project, all characteristics are known, including annual production volumes, necessary investment volumes, and profit. The total amount of investments that the investor spends on developing the field during the entire planning period we know. It is required to determine which projects to implement in each cluster so that, within the total amount of investments, the profit for the entire planning period is maximum. The problem under consideration is NP-hard. However, it is solved by dynamic programming with pseudopolynomial time complexity. Nevertheless, in practice, there are additional constraints that do not allow solving the problem with acceptable accuracy at a reasonable time. Such restrictions, in particular, are annual production volumes. In this paper, we considered only the upper constraints that are dictated by the pipeline capacity. For the investment optimization problem with such additional restrictions, we obtain qualitative results, propose an approximate algorithm, and investigate its properties. Based on the results of a numerical experiment, we conclude that the developed algorithm builds a solution close (in terms of the objective function) to the optimal one